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Logarithmic Equations Worksheet with Key

Students will practice solving logarithmic equations .

Example Questions

Solve the following Equations:

1) log 3 (4 – x) = log 3 (x + 8) log 2 (x – 2) + log 2 (x – 5) = log 2 (x – 1) + log 2 (x + 6)

Logarithmic equatiosn problem

Other Details

This is a 4 part worksheet:

  • Part I Model Problems
  • Part II Practice
  • Part III Challenge Problems
  • Part IV Answer Key
  • Logarithm Rules
  • Graph of Logarithm

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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.”

Download Solving Logarithmic Equations Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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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 Easy

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 1 Moderate

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 Easy

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.

Solve for x - Level 2 Moderate

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 - Easy

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.

Logarithmic Equations - Moderate

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.

Solving Logarithmic Equations Using a Calculator

Related Printable Worksheets

▶ Evaluating Logarithmic Expression

▶ Common Logarithms

▶ Natural Logarithms

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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.

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

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.

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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

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

Find the value of the variables in each equation..

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

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

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Course: Algebra 2   >   Unit 8

  • Solving exponential equations using logarithms: base-10

Solving exponential equations using logarithms

  • Solve exponential equations using logarithms: base-10 and base-e
  • Solving exponential equations using logarithms: base-2
  • Solve exponential equations using logarithms: base-2 and other bases

Solving exponential equations of the form a ⋅ b x = d ‍  

Check your understanding.

  • (Choice A)   x = log 2 ⁡ ( 39.3 ) ‍   A x = log 2 ⁡ ( 39.3 ) ‍  
  • (Choice B)   x = log 6 ⁡ ( 118 ) ‍   B x = log 6 ⁡ ( 118 ) ‍  
  • (Choice C)   x = log 12 ⁡ ( 236 ) ‍   C x = log 12 ⁡ ( 236 ) ‍  
  • (Choice D)   x = log 118 ⁡ ( 6 ) ‍   D x = log 118 ⁡ ( 6 ) ‍  
  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Solving exponential equations of the form a ⋅ b c x = d ‍  

  • (Choice A)   t = log ⁡ ( 43.5 ) ‍   A t = log ⁡ ( 43.5 ) ‍  
  • (Choice B)   t = log 30 ⁡ ( 130.5 ) ‍   B t = log 30 ⁡ ( 130.5 ) ‍  
  • (Choice C)   t = log ⁡ ( 174 ) 4 ‍   C t = log ⁡ ( 174 ) 4 ‍  
  • (Choice D)   t = log 30 ⁡ ( 522 ) 4 ‍   D t = log 30 ⁡ ( 522 ) 4 ‍  

Challenge problem

  • (Choice A)   2 ‍   A 2 ‍  
  • (Choice B)   3 ‍   B 3 ‍  
  • (Choice C)   4 ‍   C 4 ‍  
  • (Choice D)   log 2 ⁡ ( 3 ) ‍   D log 2 ⁡ ( 3 ) ‍  
  • (Choice E)   log 3 ⁡ ( 2 ) ‍   E log 3 ⁡ ( 2 ) ‍  
  • (Choice F)   log ⁡ ( 3 ) ‍   F log ⁡ ( 3 ) ‍  

Exponential Equations Solving with Logs Worksheets

Exponential equations, solving with logs.

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  3. Solve Logarithmic Equations Worksheet

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  4. Solving Log Equations Worksheets

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  5. Logarithmic Equations Worksheet With Answers

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  6. Solving Logarithmic Equations Worksheet With Answers

    solve log equations worksheet

VIDEO

  1. Time and work Best Solution||(कार्य तथा समय)||Solve in 10 sec.|| rrb ALP||rrb RPF||ssc|| cgl

  2. Algebra: Solve log with exponentials

  3. Solve log equations

  4. #19, Solve log/exp equations, MAY 1

  5. Quick Review: How to Solve Log Equations

  6. Algebra

COMMENTS

  1. PDF Logarithmic Equations Date Period

    Solve each equation. 1) log 5 x = log (2x + 9) {3} 2) log (10 − 4x) = log (10 − 3x) {0} 3) log (4p − 2 ... Xrwivg yh5tFsZ 4r dels LeWrVv7e Edy. 7 f iM 9axd Vev owti 7t Jho SI gnbfGiun 5intke q iA Ll Ygre Pb GrwaT E2l. i Worksheet by Kuta Software LLC 13) log (16 + 2 b) = log (b2 − 4b) {8, −2} 14) ln (n2 + 12) = ln (−9n − 2) {−2 ...

  2. PDF Worksheet: Logarithmic Function

    Worksheet: Logarithmic Function 1. Find the value of y. (1) log 5 25 = y (2) log 3 1 = y (3 ... log(a b) = loga logb (3) logxk = k logx (4) (loga)(logb) = log(a+b) (5) loga logb = log(a b) (6) (lna)k = k lna (7) log a a a = a (8) ln 1 x = lnx (9) lnp x x k = 2k 7. Solve the following logarithmic equations. (1) lnx = 3 (2) log(3x 2) = 2 (3 ...

  3. Logarithmic Equations Worksheets

    10.\:\:\log_{3}(\log_{2}(x))=1 Study Tools AI Math Solver Popular Problems Worksheets Study Guides Practice Cheat Sheets Calculators Graphing Calculator Geometry Calculator Company About Symbolab Blog Help Contact Us

  4. PDF Logarithmic Equations

    Solve each equation. 5) log ... Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com. Title: document1 Author: Mike Created Date: 5/23/2016 2:21:09 PM ...

  5. PDF Logarithmic Equations

    solving logarithm equations . Logarithmic Equations, Level I . Purpose: This is intended to refresh your skills in solving logarithmic equations. Activity: Work through the following activity and examples. Do all of the practice problems before . consulting with a tutor. • Definition: for . b ,b >≠0 1, log a x b = is equivalent to ba x ...

  6. PDF Logarithmic Equations

    Logarithmic Equations Version 1 Name: _____ Date: _____ Score: _____ 2 2 2 x 1) log 2 log 5 log 5 x 1 3 3 3 x x x ... 3) log 4 log 4 1 55 x x x 2 x 5 4) log 1 1 2 2 x x 3 Direction: Solve each logarithmic equations. Check your solutions to exclude extraneous answers. Show all your answer in the space provided. Author:

  7. Logarithmic Equations Worksheet with Key

    All of your worksheets are now here on Mathwarehouse.com. Please update your bookmarks! ... Solve the following Equations: 1) log 3 (4 - x) = log 3 (x + 8) log 2 (x - 2) + log 2 (x - 5) = log 2 (x - 1) + log 2 (x + 6) Other Details. This is a 4 part worksheet: Part I Model Problems; Part II Practice; Part III Challenge Problems; Part IV ...

  8. Solving Logarithmic Equations

    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. ALWAYScheck your solved values with the original logarithmic equation.

  9. PDF Solving Logarithm Equations Worksheet

    Solving Logarithm Equations Worksheet Name_____ ©Y ]2U0f1W7U VKEuEtIaj NSPohf_tPw]aKrMeL WLVLMCf.p n wAKljll Pr[iqghhEt\sP srqegsSeVrOvUegdR. Solve each equation. 1) 9log 9 v = 0 2) -log 9 n = 1 3) -7 - 10log 6 r = -274) 7log 5 x - 4 = 17 5) -4log 6-r = -4 6) -4 + log 2-8p = -3 7) 4 - 8log 7 2x = -288) 6 + 3log ...

  10. Solving Logarithmic Equations Worksheets

    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

  11. Logarithmic Equations Worksheets

    Equations. 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 ...

  12. PDF Logarithmic Equations Date Period

    Solve each equation. 1) log ... Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com. Title: document1 Author: Mike Created Date: 5/23/2016 2:20:58 PM ...

  13. PDF Solving Logarithmic Equations

    Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www.EffortlessMath.com Solving Logarithmic Equations Find the value of the variables in each equation.

  14. LOGARITHMS

    There are a couple of ways to solve a logarithmic equation. One method is to get all logs to the left side of the equal sign and condense the problem so there is only one log. The next step would be to write the problem in exponential form and solve. Another method involves one of the properties of simple logarithms.

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

    A 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.

  16. IXL

    Recommendations. Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve logarithmic equations I" and thousands of other math skills.

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

    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 ...

  18. Solving exponential equations using logarithms

    To solve for x , we must first isolate the exponential part. To do this, divide both sides by 5 as shown below. We do not multiply the 5 and the 2 as this goes against the order of operations! 5 ⋅ 2 x = 240 2 x = 48. Now, we can solve for x by converting the equation to logarithmic form. 2 x = 48 is equivalent to log 2.

  19. PDF Evaluating Logarithms

    Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Evaluating Logarithms Name_____ Date_____ Period____ Evaluate each expression. 1) log 2) log 3) log 4) log 5) log 6) log 7) log 8) log 9) log 10) log 11) log 12) log Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com

  20. Logarithmic Equation Calculator

    To solve a logarithmic equations use the esxponents rules to isolate logarithmic expressions with the same base. Set the arguments equal to each other, solve the equation and check your answer. ... Study Tools AI Math Solver Popular Problems Worksheets Study Guides Practice Cheat Sheets Calculators Graphing Calculator Geometry Calculator ...

  21. PDF Solving Exponential Equations with Logarithms

    Solve each equation. Round your answers to the nearest ten-thousandth. 1) 3 b = 17 2.5789 2) 12 r = 13 1.0322 3) 9n = 49 1.7712 4) 16 v = 67 1.5165 5) 3a = 69 3.854 6) 6r = 51 ... Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com. Title: Solving Exponential Equations with Logarithms

  22. Exponential Equations Solving with Logs Worksheets

    worksheets for pre-algebra,algebra,calculus,functions