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Exponential and Logarithmic Equations

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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

Correct Answer: D

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

Correct Answer: B

3. . Solve the following exponential equation for x.

2 ∙ 53x = 250
  1. 1/3
  2. 1/2
  3. 1
  4. 2

Correct Answer: C

4. . Solve the following exponential equation for x.

7 ∙ 23x - 4 = 28
  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: B

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

Correct Answer: D

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

Correct Answer: A

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

Correct Answer: A

8. . Solve the following equation for x.

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

Correct Answer: C

9. . Solve the following equation for x.

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

Correct Answer: B

10. . Solve the following equation for x.

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

Correct Answer: B

11. . Solve the following equation for x.

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

Correct Answer: D

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

Correct Answer: A

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

Correct Answer: A

14. . Solve the following logarithmic equation for x.

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

Correct Answer: C

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

Correct Answer: C

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  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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