# Exponential and Logarithmic Equations

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The following math revision questions are provided in support of the math tutorial on Exponential and Logarithmic Equations. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Exponential and Logarithmic Equations tutorials. The Exponential and Logarithmic Equations calculators are particularly useful for ensuring your step-by-step calculations are correct as well as ensuring your final result is accurate.

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Logarithms Learning Material
Tutorial IDTitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
13.2Exponential and Logarithmic Equations

## Exponential and Logarithmic Equations Revision Questions

1. . What is the value of the variable x in the exponential equation

3 ∙ 2x = 96
1. 12
2. 8
3. 6
4. 5

2. . What is the value of the variable x in the exponential equation

18/32x = 2
1. 1/2
2. 1
3. 2
4. 3

3. . Solve the following exponential equation for x.

2 ∙ 53x = 250
1. 1/3
2. 1/2
3. 1
4. 2

4. . Solve the following exponential equation for x.

7 ∙ 23x - 4 = 28
1. 1
2. 2
3. 3
4. 4

5. . Solve the following exponential equation for x. Write the result to three decimal places.

2x = 6
1. 3.000
2. 2.250
3. 2.225
4. 2.219

6. . What is the value of x in the equation

3-4x = 10/9
1. 1/2 - 1/log 81
2. 1/log 81
3. log 81
4. log3 10

7. . What is/are the value(s) of x in the following exponential equation

2x2 - 5 = 1/16
1. -1 and 1
2. 1 only
3. -1 only
4. 0 and 1

8. . Solve the following equation for x.

log4 2x = 3
1. 12
2. 24
3. 32
4. 64

9. . Solve the following equation for x.

log2 (3x - 1) = log2 20
1. 21
2. 7
3. 27
4. 210

10. . Solve the following equation for x.

log3 (2x - 1) = 2 log3 x
1. -1
2. 1
3. 2
4. 4

11. . Solve the following equation for x.

log5 (1 - 4x) = log25 1
1. 4
2. 1
3. 0
4. 1/4

### More challenging questions

12. . Solve the following exponential equation for x.

5x = 2x + 2
1. 2 log5 2/1 - log5 2
2. 1 - log5 2
3. log5 2/1 - log5 2
4. 2

13. . Solve the following exponential equation for x.

(1/3)2x = 12
1. log 9/log 12
2. log 12/log 9
3. log3 4
4. log 4/3

14. . Solve the following logarithmic equation for x.

log2 (√2 ∙ x) = log4 (12x - 18)
1. 1
2. 2
3. 3
4. 4

15. . Solve the following logarithmic equation for x.

log3 9/log x = log x/log2 256
1. 100
2. 1,000
3. 10,000
4. 100,000

## Whats next?

Enjoy the "Exponential and Logarithmic Equations" practice questions? People who liked the "Exponential and Logarithmic Equations" practice questions found the following resources useful:

1. Practice Questions Feedback. Helps other - Leave a rating for this practice questions (see below)
2. Logarithms Math tutorial: Exponential and Logarithmic Equations. Read the Exponential and Logarithmic Equations math tutorial and build your math knowledge of Logarithms
3. Logarithms Video tutorial: Exponential and Logarithmic Equations. Watch or listen to the Exponential and Logarithmic Equations video tutorial, a useful way to help you revise when travelling to and from school/college
4. Logarithms Revision Notes: Exponential and Logarithmic Equations. Print the notes so you can revise the key points covered in the math tutorial for Exponential and Logarithmic Equations
5. Check your calculations for Logarithms questions with our excellent Logarithms calculators which contain full equations and calculations clearly displayed line by line. See the Logarithms Calculators by iCalculator™ below.
6. Continuing learning logarithms - read our next math tutorial: Modelling Curves using Logarithms

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