solve log equations worksheet

Solving Logarithmic Equations Worksheets

Solving logarithmic equations worksheets are about logarithms, which is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. "Proportional to the logarithm to the base 10 of the concentration."

Benefits of Solving Logarithmic Equations Worksheets

A logarithm is defined as the power to which number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction. We will learn more about it in the benefits of solving logarithmic equations worksheets.

“The logarithm of a positive real number a with respect to base b, a positive real number not equal to 1[nb 1], is the exponent by which b must be raised to yield a.”

That means, by = a and it is read as “the logarithm of a to base b.”

Logarithmic Equations Worksheets - Download free PDFs

Logarithmic equations, different bases, nested logs.

Please add a message.

Message received. Thanks for the feedback.

Search Functionality Update!

To optimize your search experience, please refresh the page.

Windows: Press Ctrl + F5

Mac: Use Command + Shift+ R or Command + Option + R

Mobile: Tap and hold the refresh icon, then select "Hard Refresh" or "Reload Without Cache" for an instant upgrade!

• Child Login
• Number Sense
• Measurement
• Pre Algebra
• Figurative Language
• Reading Comprehension
• Reading and Writing
• Science Worksheets
• Social Studies Worksheets
• Math Worksheets
• ELA Worksheets
• Online Worksheets

Browse By Grade

• Become a Member

• Kindergarten

• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even Numbers
• Prime and Composite Numbers
• Roman Numerals
• Ordinal Numbers

• Big vs Small
• Long vs Short
• Tall vs Short
• Heavy vs Light
• Full, Half-Full, or Empty
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature

• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem and Leaf Plot
• Box and Whisker Plot
• Permutations
• Combinations

• Lines, Rays, and Line Segments
• Points, Lines, and Planes
• Transformation
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel and Perpendicular Lines
• Surface Area
• Pythagorean Theorem

• Significant Figures
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Scientific Notation
• Absolute Value

• Translating Algebraic Phrases
• Simplifying Algebraic Expressions
• Evaluating Algebraic Expressions
• Systems of Equations
• Slope of a Line
• Equation of a Line
• Quadratic Equations
• Polynomials
• Inequalities
• Determinants
• Arithmetic Sequence
• Arithmetic Series
• Geometric Sequence
• Complex Numbers
• Trigonometry

Logarithmic Equations Worksheets

• Pre-Algebra >
• Logarithms >

Make use of our free, printable logarithmic equations worksheets to understand how to solve equations with a log on one side by applying the inverse relationship between logarithms and exponents, and to practice solving equations with logs on both sides by setting the arguments equal. This set also includes resources to solve log equations using a calculator.

These pdf logarithmic equations worksheets are recommended for high school students.

Solve for x: Level 1 Easy

Kick off practice with level 1, where students write logarithmic equations with an unknown base, argument, or exponent in the exponential form and solve for x.

Solve for x: Level 1 Moderate

Determine the value of x in these moderate-level log equations worksheet pdfs where the arguments are raised to powers that may be either integers or fractions.

Solve for x: Level 2 Easy

Get a jump on your peers with this level 2 set featuring logarithmic equations with algebraic expressions that require high school students to flex their prowess in the topic as they solve for x.

Solve for x:Level 2 Moderate

Take on the challenge of these moderately difficult, printable worksheets on logarithmic equations, where high school children solve for the unknown variable.

Logarithmic Equations - Easy

Can you solve equations with logs on both sides? Key into the fact that when logs on either side have the same base, we can equate the arguments. Solve with swagger!

Logarithmic Equations - Moderate

A delight for math enthusiasts, these printable logarithmic equations worksheets are sure to help practice sessions shift up a gear with moderately difficult exercises.

Solving Logarithmic Equations Using a Calculator

High school kids are sure to breeze through these pdf worksheets on solving logarithmic equations using a calculator! Turn the logs into exponents and solve the equations with a calculator.

Related Printable Worksheets

▶ Evaluating Logarithmic Expression

▶ Common Logarithms

▶ Natural Logarithms

Tutoringhour

What we offer, information.

• Membership Benefits
• How to Use Online Worksheets
• How to Use Printable Worksheets
• Printing Help
• Testimonial
• Privacy Policy
• Refund Policy

Copyright © 2024 - Tutoringhour

You must be a member to unlock this feature!

Sign up now for only $29.95/year — that's just 8 cents a day!

Printable Worksheets

• 20,000+ Worksheets Across All Subjects
• Access to Answer Key
• Add Worksheets to "My Collections"
• Create Custom Workbooks

Digitally Fillable Worksheets

• 1100+ Math and ELA Worksheets
• Preview and Assign Worksheets
• Create Groups and Add Children
• Track Progress

Logarithmic Equations

Solving logarithmic equations.

Generally, there are two types of logarithmic equations. Study each case carefully before you start looking at the worked examples below.

Types of Logarithmic Equations

• The first type looks like this.

If you have a single logarithm on each side of the equation having the same base, you can set the arguments equal to each other and then solve. The arguments here are the algebraic expressions represented by [latex]\color{blue}M[/latex] and [latex]\color{red}N[/latex].

• The second type looks like this.

If you have a single logarithm on one side of the equation, you can express it as an exponential equation and solve it .

Let’s learn how to solve logarithmic equations by going over some examples.

Examples of How to Solve Logarithmic Equations

Example 1: Solve the logarithmic equation.

Since we want to transform the left side into a single logarithmic equation, we should use the Product Rule in reverse to condense it. Here is the rule, just in case you forgot.

• Apply Product Rule from Log Rules .
• Distribute: [latex]\left( {x + 2} \right)\left( 3 \right) = 3x + 6[/latex]
• Drop the logs, set the arguments (stuff inside the parenthesis) equal to each other.
• Then solve the linear equation. I know you got this part down!

Just a big caution. ALWAYS check your solved values with the original logarithmic equation.

• It is OKAY for [latex]x[/latex] to be [latex]0[/latex] or negative.
• However, it is NOT ALLOWED to have a logarithm of a negative number or a logarithm of zero, [latex]0[/latex], when substituted or evaluated into the original logarithm equation.

CAUTION: The logarithm of a negative number, and the logarithm of zero are both not defined .

[latex]{\log _b}\left( {{\rm{negative\,\,number}}} \right) = {\rm{undefined}}[/latex]

[latex]{\log _b}\left( 0 \right) = {\rm{undefined}}[/latex]

Let’s check our answer to see if [latex]x=7[/latex] is a valid solution. Substitute it back into the original logarithmic equation and verify if it yields a true statement.

Yes! Since [latex]x = 7[/latex] checks, we have a solution at [latex]\color{blue}x = 7[/latex].

  Example 2: Solve the logarithmic equation.

Start by condensing the log expressions on the left into a single logarithm using the Product Rule. We want to have a single log expression on each side of the equation. Be ready though to solve for a quadratic equation since [latex]x[/latex] will have a power of [latex]2[/latex].

• Apply Product Rule from Log Rules
• Simplify: [latex]\left( x \right)\left( {x – 2} \right) = {x^2} – 2x[/latex]
• Drop the logs, set the arguments (stuff inside the parenthesis) equal to each other
• Solve the quadratic equation using the factoring method . But you need to move everything on one side while forcing the opposite side equal to [latex]0[/latex].
• Set each factor equal to zero, then solve for [latex]x[/latex].

[latex]x – 5 = 0[/latex] implies that [latex]x = 5[/latex]

[latex]x + 2 = 0[/latex] implies that [latex]x = – 2[/latex]

So the possible solutions are [latex]x = 5[/latex] and [latex]x = – 2[/latex].  Remember to always substitute the possible solutions back to the original log equation.

Let’s check our potential answers [latex]x = 5[/latex] and [latex]x = – 2[/latex] if they will be valid solutions.

After checking our values of [latex]x[/latex], we found that [latex]x = 5[/latex] is definitely a solution. However, [latex]x =-2[/latex] generates negative numbers inside the parenthesis ( log of zero and negative numbers are undefined) which makes us eliminate [latex]x =-2[/latex] as part of our solution.

Therefore, the final solution is just [latex]\color{blue}x=5[/latex]. We disregard [latex]x=-2[/latex] because it is an extraneous solution.

Example 3: Solve the logarithmic equation.

This is an interesting problem. What we have here are differences of logarithmic expressions on both sides of the equation. Simplify or condense the logs on both sides by using the Quotient Rule.

• The difference of logs is telling us to use the Quotient Rule . Convert the subtraction operation outside into a division operation inside the parenthesis. Do it to both sides of the equations.
• I think we are ready to set each argument equal to each other since we can reduce the problem to have a single log expression on each side of the equation.
• Drop the logs, and set the arguments (stuff inside the parenthesis) equal to each other. Note that this is a Rational Equation . One way to solve it is to get its Cross Product .
• It looks like this after getting its Cross Product.
• Simplify both sides by the Distributive Property. At this point, we realize that it is just a Quadratic Equation. No big deal then. Move everything to one side, which forces one side of the equation to be equal to zero.
• This is easily factorable. Now set each factor to zero and solve for [latex]x[/latex].
• So, these are our possible answers.

I will leave it to you to check our potential answers back into the original log equation. You should verify that [latex]\color{blue}x=8[/latex] is the only solution, while [latex]x =-3[/latex] is not since it generates a scenario wherein we are trying to get the logarithm of a negative number. Not good!

Example 4: Solve the logarithmic equation.

If you see “log” without an explicit or written base, it is assumed to have a base of [latex]10[/latex]. In fact, a logarithm with base [latex]10[/latex] is known as the common logarithm .

What we need is to condense or compress both sides of the equation into a single log expression. On the left side, we see a difference of logs which means we apply the Quotient Rule while the right side requires the Product Rule because they’re the sum of logs.

There’s just one thing that you have to pay attention to on the left side. Do you see that coefficient [latex]\Large{1 \over 2}\,[/latex]?

Well, we have to bring it up as an exponent using the Power Rule in reverse.

• Bring up that coefficient [latex]\large{1 \over 2}[/latex] as an exponent (refer to the leftmost term)
• Simplify the exponent (still referring to the leftmost term)
• Then, condense the logs on both sides of the equation. Use the Quotient Rule on the left and Product Rule on the right.
• Here, I used different colors to show that since we have the same base (if not explicitly shown it is assumed to be base [latex]10[/latex]), it’s okay to set them equal to each other.
• Dropping the logs and just equating the arguments inside the parenthesis.
• At this point, you may solve the Rational Equation by performing Cross Product. Move all the terms on one side of the equation, then factor them out.
• Set each factor equal to zero and solve for [latex]x[/latex].

It’s time to check your potential answers. When you check [latex]x=0[/latex] back into the original logarithmic equation, you’ll end up having an expression that involves getting the logarithm of zero, which is undefined, meaning – not good! So, we should disregard or drop [latex]\color{red}x=0[/latex] as a solution.

Checking [latex]\Large{x = {3 \over 4}}[/latex], confirms that indeed [latex]\Large{\color{blue}{x = {3 \over 4}}}[/latex] is the only solution .

Example 5: Solve the logarithmic equation.

This problem involves the use of the symbol [latex]\ln[/latex] instead of [latex]\log[/latex] to mean logarithm.

Think of [latex]\ln[/latex] as a special kind of logarithm using base [latex]e[/latex] where [latex]e \approx 2.71828[/latex].

• Use Product Rule on the right side
• Write the variable first, then the constant to be ready for the FOIL method .
• Simplify the two binomials by multiplying them together.
• At this point, I simply color-coded the expression inside the parenthesis to imply that we are ready to set them equal to each other.
• Yep! This is where we say that the stuff inside the left parenthesis equals the stuff inside the right parenthesis.
• Solve the Quadratic Equation using the Square Root Method . You do it by isolating the squared variable on one side and the constant on the other. Then we apply the square root on both sides.

Don’t forget the [latex]\pm[/latex] symbol.

• Simplifying further, we should get these possible answers.

Check if the potential answers found above are possible answers by substituting them back to the original logarithmic equations.

You should be convinced that the ONLY valid solution is [latex]\large{\color{blue}x = {1 \over 2}}[/latex] which makes [latex]\large{\color{red}x = -{1 \over 2}}[/latex] an extraneous answer.

Example 6: Solve the logarithmic equation.

There is only one logarithmic expression in this equation. We consider this as the second case wherein we have

We will transform the equation from the logarithmic form to the exponential form, then solve it.

• I color-coded the parts of the logarithmic equation to show where they go when converted into exponential form.
• The blue expression stays at its current location, but the red number becomes the exponent of the base of the logarithm which is [latex]3[/latex].
• Simplify the right side, [latex]{3^4} = 81[/latex].
• Finish off by solving the two-step linear equation that arises.

You should verify that the value [latex]\color{blue}x=12[/latex] is indeed the solution to the logarithmic equation.

Example 7: Solve the logarithmic equation.

Collect all the logarithmic expressions on one side of the equation (keep it on the left) and move the constant to the right side. Use the Quotient Rule to express the difference of logs as fractions inside the parenthesis of the logarithm.

• Move all the logarithmic expressions to the left of the equation, and the constant to the right.
• Use the Quotient Rule to condense the log expressions on the left side.
• Get ready to write the logarithmic equation into its exponential form.
• The blue expression stays in its current location, but the red constant turns out to be the exponent of the base of the log.
• Simplify the right side of the equation since [latex]5^{\color{red}1}=5[/latex].
• This is a Rational Equation due to the presence of variables in the numerator and denominator.

I would solve this equation using the Cross Product Rule. But I have to express first the right side of the equation with the explicit denominator of [latex]1[/latex]. That is, [latex]5 = {\large{{5 \over 1}}}[/latex]

• Perform the Cross-Multiplication and then solve the resulting linear equation.

When you check [latex]x=1[/latex] back to the original equation, you should agree that [latex]\large{\color{blue}x=1}[/latex] is the solution to the log equation.

Example 8: Solve the logarithmic equation.

This problem is very similar to #7. Let’s gather all the logarithmic expressions to the left while keeping the constant on the right side. Since we have the difference of logs, we will utilize the Quotient Rule.

• Move the log expressions to the left side, and keep the constant to the right.
• Apply the Quotient Rule since they are the difference of logs.
• I used different colors here to show where they go after rewriting in exponential form.
• Notice that the expression inside the parenthesis stays in its current location, while the [latex]\color{red}5[/latex] becomes the exponent of the base.
• To solve this Rational Equation, apply the Cross Product Rule.
• Simplify the right side by the distributive property . It looks like we are dealing with a quadratic equation.
• Move everything to the left side and make the right side just zero.

Factor out the trinomial. Set each factor equal to zero then solve for [latex]x[/latex].

• When you solve for [latex]x[/latex], you should get these values of [latex]x[/latex] as potential solutions.

Make sure that you check the potential answers from the original logarithmic equation.

You should agree that [latex]\color{blue}x=-32[/latex] is the only solution. That makes [latex]\color{red}x=4[/latex] an extraneous solution, so disregard it.

Example 9: Solve the logarithmic equation

I hope you’re getting the main idea now on how to approach this type of problem. Here we see three log expressions and a constant. Let’s separate the log expressions and the constant on opposite sides of the equation.

• Let’s keep the log expressions on the left side while the constant on the right side.
• Start by condensing the log expressions using the Product Rule to deal with the sum of logs.
• Then further condense the log expressions using the Quotient Rule to deal with the difference of logs.
• At this point, I used different colors to illustrate that I’m ready to express the log equation into its exponential equation form.
• Keep the expression inside the grouping symbol ( blue ) in the same location while making the constant [latex]\color{red}1[/latex] on the right side as the exponent of the base [latex]7[/latex].
• Solve this Rational Equation using Cross Product. Express [latex]7[/latex] as [latex]\large{7 \over 1}[/latex].
• Cross multiply.
• Move all terms to the left side of the equation. Factor out the trinomial. Next, set each factor equal to zero and solve for [latex]x[/latex].
• These are your potential answers. Always check your values.

It’s obvious that when we plug in [latex]x=-8[/latex] back into the original equation, it results in a logarithm with a negative number. Therefore, you exclude [latex]\color{red}x=-8[/latex] as part of your solution.

Thus, the only solution is [latex]\color{blue}x=11[/latex].

Example 10: Solve the logarithmic equation.

• Keep the log expression on the left, and move all the constants on the right side.
• I think we’re ready to transform this log equation into the exponential equation.
• The expression inside the parenthesis stays in its current location while the constant [latex]3[/latex] becomes the exponent of the log base [latex]3[/latex].
• Simplify the right side since [latex]{3^3}=27[/latex]. What we have here is a simple Radical Equation .

Check this separate lesson if you need a refresher on how to solve different types of Radical Equations .

• To get rid of the radical symbol on the left side, square both sides of the equation.
• After squaring both sides, it looks like we have a linear equation. Just solve it as usual.

Check your potential answer back into the original equation.

After doing so, you should be convinced that indeed [latex]\color{blue}x=-104[/latex] is a valid solution.

You may also be interested in these related math lessons or tutorials:

Condensing Logarithms

Expanding Logarithms

Logarithm Explained

Logarithm Rules

Solving Logarithmic Equations

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Logarithm Worksheets (pdfs)

Free worksheets with answer keys.

Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Logarithmic Equations Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

• + ACCUPLACER Mathematics
• + ACT Mathematics
• + AFOQT Mathematics
• + ALEKS Tests
• + ASVAB Mathematics
• + ATI TEAS Math Tests
• + Common Core Math
• + DAT Math Tests
• + FSA Tests
• + FTCE Math
• + GED Mathematics
• + Georgia Milestones Assessment
• + GRE Quantitative Reasoning
• + HiSET Math Exam
• + HSPT Math
• + ISEE Mathematics
• + PARCC Tests
• + Praxis Math
• + PSAT Math Tests
• + PSSA Tests
• + SAT Math Tests
• + SBAC Tests
• + SIFT Math
• + SSAT Math Tests
• + STAAR Tests
• + TABE Tests
• + TASC Math
• + TSI Mathematics
• + ACT Math Worksheets
• + Accuplacer Math Worksheets
• + AFOQT Math Worksheets
• + ALEKS Math Worksheets
• + ASVAB Math Worksheets
• + ATI TEAS 6 Math Worksheets
• + FTCE General Math Worksheets
• + GED Math Worksheets
• + 3rd Grade Mathematics Worksheets
• + 4th Grade Mathematics Worksheets
• + 5th Grade Mathematics Worksheets
• + 6th Grade Math Worksheets
• + 7th Grade Mathematics Worksheets
• + 8th Grade Mathematics Worksheets
• + 9th Grade Math Worksheets
• + HiSET Math Worksheets
• + HSPT Math Worksheets
• + ISEE Middle-Level Math Worksheets
• + PERT Math Worksheets
• + Praxis Math Worksheets
• + PSAT Math Worksheets
• + SAT Math Worksheets
• + SIFT Math Worksheets
• + SSAT Middle Level Math Worksheets
• + 7th Grade STAAR Math Worksheets
• + 8th Grade STAAR Math Worksheets
• + THEA Math Worksheets
• + TABE Math Worksheets
• + TASC Math Worksheets
• + TSI Math Worksheets
• + AFOQT Math Course
• + ALEKS Math Course
• + ASVAB Math Course
• + ATI TEAS 6 Math Course
• + CHSPE Math Course
• + FTCE General Knowledge Course
• + GED Math Course
• + HiSET Math Course
• + HSPT Math Course
• + ISEE Upper Level Math Course
• + SHSAT Math Course
• + SSAT Upper-Level Math Course
• + PERT Math Course
• + Praxis Core Math Course
• + SIFT Math Course
• + 8th Grade STAAR Math Course
• + TABE Math Course
• + TASC Math Course
• + TSI Math Course
• + Number Properties Puzzles
• + Algebra Puzzles
• + Geometry Puzzles
• + Intelligent Math Puzzles
• + Ratio, Proportion & Percentages Puzzles
• + Other Math Puzzles

How to Solve Logarithmic Equations? (+FREE Worksheet!)

In this blog post, you will learn how to solve Logarithmic Equations using the properties of logarithms in a few easy steps.

Related Topics

• How to Solve Natural Logarithms Problems
• How to Evaluate Logarithms
• Logarithms Properties

Step-by-step guide to solving logarithmic equations

• Convert the logarithmic equation to an exponential equation when it’s possible. (If no base is indicated, the base of the logarithm is \(10\))
• Condense logarithms if you have more than one log on one side of the equation.
• Plug the answers back into the original equation and check if the solution works.

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Logarithmic equations – example 1:.

Find the value of the variables in each equation. \(\log_{4}{(20-x^2)}=2\)

Use log rule: \(\log_{b}{x}=\log_{b}{y}\), then: \(x=y\)

\(2=\log_{4}{4^2},\log_{4}{(20-x^2)}=\log_{4}{4^2}=\log_{4}{16}\)

then: \(20-x^2=16→20-16=x^2→x^2=4→x=2\) or \(x=-2\)

Logarithmic Equations – Example 2:

Find the value of the variables in each equation. \(log⁡(2x+2)=log⁡(4x-6)\)

When the logs have the same base: \(f(x)=g(x)\),then: \(ln(f(x))=ln(g(x))\),

\(log⁡(2x+2)=log⁡(4x-6)→2x+2=4x-6→2x+2-4x+6=0\)

\(2x+2-4x+6=0→-2x+8=0→-2x=-8→x=\frac{-8}{-2}=4\)

Logarithmic Equations – Example 3:

Find the value of the variables in each equation. \(\log_{2}{(25-x^2)}=2\)

\(2=\log_{2}{2^2},\log_{2}{(25-x^2)}=\log_{2}{2^2}=\log_{2}{4}\)

Then: \(25-x^2=4→25-4=x^2→x^2=21 →x=\sqrt{21} \) or \(-\sqrt{21}\)

Logarithmic Equations – Example 4:

Find the value of the variables in each equation. \(log⁡(8x+3)=log⁡(2x-6)\)

\(log⁡(8x+3)=log⁡(2x-6)→8x+3=2x-6→8x+3-2x+6=0\)

\(6x+9=0→6x=-9→x=\frac{-9}{6}=-\frac{3}{2}\) Logarithms of negative numbers are not defined. Therefore, there is no solution for this equation.

Exercises for Logarithmic Equations

The Best Math Book to Help You Ace the Math Test

Algebra I for Beginners The Ultimate Step by Step Guide to Acing Algebra I

Find the value of the variables in each equation..

• \(\color{blue}{log⁡(x+5)=2}\)
• \(\color{blue}{log x-log 4=3}\)
• \(\color{blue}{log x+log 2=4}\)
• \(\color{blue}{log 10+log x=1}\)
• \(\color{blue}{log x+log 8=log 48}\)
• \(\color{blue}{-3\log_{3}{(x-2)}=-12}\)
• \(\color{blue}{log 6x=log (x+5)}\)
• \(\color{blue}{log (4k-5)=log (2k-1)}\)
• \(\color{blue}{95}\)
• \(\color{blue}{4000}\)
• \(\color{blue}{5000}\)
• \(\color{blue}{1}\)
• \(\color{blue}{6}\)
• \(\color{blue}{83}\)
• \(\color{blue}{2}\)

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Pre-algebra in 10 days the most effective pre-algebra crash course, college algebra practice workbook the most comprehensive review of college algebra, high school algebra i a comprehensive review and step-by-step guide to mastering high school algebra 1, 10 full length clep college algebra practice tests the practice you need to ace the clep college algebra test.

by: Effortless Math Team about 5 years ago (category: Articles , Free Math Worksheets )

Effortless Math Team

Related to this article, more math articles.

• How to Use Arrays to Divide Two-Digit Numbers by One-digit Numbers
• Unlocking the Secrets of Inverse Functions: A Closer Look
• ASVAB Math FREE Sample Practice Questions
• Top 10 6th Grade OST Math Practice Questions
• Newton’s Technique to Fish Out the Roots
• GED Calculator Guide: Learn How To Use The TI-30XS
• How to Do Percentage Calculations? (+FREE Worksheet!)
• Hands-On Learning: How to Represent Subtraction of Fractions with Unlike Denominators Using Everyday Objects
• 8th Grade MCA Math Worksheets: FREE & Printable
• How is the FTCE General Knowledge Test Scored?

What people say about "How to Solve Logarithmic Equations? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Pre-Algebra Practice Workbook The Most Comprehensive Review of Pre-Algebra

Algebra i practice workbook the most comprehensive review of algebra 1, algebra ii practice workbook the most comprehensive review of algebra 2, algebra ii for beginners the ultimate step by step guide to acing algebra ii, pre-algebra for beginners the ultimate step by step guide to preparing for the pre-algebra test, pre-algebra tutor everything you need to help achieve an excellent score.

• ATI TEAS 6 Math
• ISEE Upper Level Math
• SSAT Upper-Level Math
• Praxis Core Math
• 8th Grade STAAR Math

Limited time only!

Save Over 45 %

It was $89.99 now it is $49.99

Login and use all of our services.

Effortless Math services are waiting for you. login faster!

Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

• Math Worksheets
• Math Courses
• Math Topics
• Math Puzzles
• Math eBooks
• GED Math Books
• HiSET Math Books
• ACT Math Books
• ISEE Math Books
• ACCUPLACER Books
• Premium Membership
• Youtube Videos

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

• Bulk Orders
• Refund Policy

SOLVING LOGARITHMIC EQUATIONS WORKSHEET

Problem 1 : 

Solve  for x :

Problem 2 : 

Solve for y :

Problem 3 :

Solve for z :

log z 8 √2  = 7

Problem 4 :  

Solve for k :

-3 =  log k 0.001

Problem 5 :

Solve for x :

log 5 [5log 3 (x)] = 2

Problem 6 :

Solve for m :

m + 2log 27 (9)   = 0

Problem 7 :

If 2log(y) = 4log(3) ,  then find the value of y . 

Problem 8 :

If 3p is equal to log(0.3) to the base 9 , then find the value of p .

Problem 9 :

Solve for r :

Problem 10 :

Solve for q :

Problem 11 :

Solve for v :

log 4 (v + 4) + log 4 8 = 2

Problem 12 :

Solve for w :

log 6 (w + 4) - log 6 (w - 1) = 1

Problem 13 :

Solve for g :

Problem 14 :

81 √ x  = log 2 (512)

1. Answer :

Convert it to exponential form.

2. Answer :

3. Answer :

Convert it to exponential form. 

125 √5  = z 7

 2 ⋅ 2 ⋅ 2 ⋅ √2 = x 7

Each 2 can be expressed as (√2 ⋅ √2).

√2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 ⋅ √2 = x 7

√2 7  = x 7

Because the exponents are equal, bases can be equated. 

x =  √2

4. Answer :

-3 = log k 0.001

k -3  = 0.001

Take reciprocal on both sides. 

k 3  = 1000 

k 3  = 10 3

5. Answer :

5log 3 (x) = 5 2

5log 3 (x) = 25

Divide both sides by 5 .

log 3 (x) = 5

6. Answer :

m = -2log 27 (9)

x = log 27 (9 -2 )

27 x  = 9 -2

(3 3 ) x  = (3 2 ) -2

3 3x  = 3 -4

Because the bases are equal, exponents can be equated. 

7. Answer :

2log(y) = 4log(3)

Divide each side by 2.

log(y) = 2log(3)

log(y) = log( 3 2 )

log(y) = log(9)

8. Answer :

From the information given, we have

3p = log 9 (0.3)

Solve for p .

9. Answer :

7r - 4 = 5(r + 2)

7r - 4 = 5r + 10

2r - 4 = 10

10. Answer :

11. Answer :

log 4 [8(v + 4)] = 2

log 4 (8v + 32) = 2

8v + 32 = 4 2

8v + 32 = 16

12. Answer :

w + 4 = 6(w - 1)

w + 4 = 6w - 6

-5w + 4 = -6

13. Answer :

log 2 (g) = 1

14. Answer :

81 √ x  = log 2 (2 9 )

81 √ x  = 9log 2 (2)

(9 2 ) √ x  = 9(1)

9 2 √ x   = 9 1

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

Derivative problems and solutions (part - 1).

Jun 30, 24 11:56 PM

Algebra Word Problems Involving Geometry (Video Solutions)

Jun 30, 24 01:17 PM

SAT Math Video Solutions (Part - 1)

Jun 30, 24 10:04 AM