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Exponential and Logarithmic Functions Practice Tests

These Grade 11 Math practice tests build fluency with exponent rules, exponential equations, logarithm definitions and properties, graph transformations, growth and decay, compound interest, and exponential models.

Skills covered

  • Using zero, negative, product, quotient, and power exponent rules
  • Solving exponential equations by rewriting with common bases
  • Evaluating logarithms and converting between logarithmic and exponential forms
  • Expanding logarithms, identifying domains, analyzing asymptotes, and transforming graphs
  • Interpreting growth, decay, half-life, compound interest, and exponential regression models

How to use these practice tests

Write the base and domain restrictions first. Use equivalent exponential or logarithmic forms, apply properties carefully, and check whether the result fits the model and its context.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Exponential and Logarithmic Functions Practice Tests

Practice Grade 11 Math questions about exponent rules, exponential equations, logarithms, graph transformations, growth and decay, and real-world models.

Choose the best answer. Apply exponent and logarithm properties, preserve domain restrictions, and interpret exponential models in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Which property expands log⁡b(MN)\log_b(MN)?

Please select an answer first.

Correct answer: A

The correct answer is log⁡bM+log⁡bN\log_b M+\log_b N.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The product property changes the logarithm of a product into the sum of the logarithms.
  3. Check the result: The correct answer is log⁡bM+log⁡bN\log_b M+\log_b N.

The product property changes the logarithm of a product into the sum of the logarithms.

2. QuestionMultiple choice

Which property expands log⁡b(MN)\log_b\left(\frac{M}{N}\right)?

Please select an answer first.

Correct answer: B

The correct answer is log⁡bM−log⁡bN\log_b M-\log_b N.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The quotient property changes division inside a logarithm into subtraction.
  3. Check the result: The correct answer is log⁡bM−log⁡bN\log_b M-\log_b N.

The quotient property changes division inside a logarithm into subtraction.

3. QuestionMultiple choice

Which property expands log⁡b(Mp)\log_b(M^p)?

Please select an answer first.

Correct answer: C

The correct answer is plog⁡bMp\log_b M.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The power property moves the exponent to the coefficient: log base b of M^p = p log base b of M.
  3. Check the result: The correct answer is plog⁡bMp\log_b M.

The power property moves the exponent to the coefficient: log base b of M^p = p log base b of M.

4. QuestionMultiple choice

What is the domain of f(x)=log⁡(x−2)f(x)=\log(x-2)?

Please select an answer first.

Correct answer: D

The correct answer is x>2x>2.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: A logarithm requires a positive argument, so x - 2 > 0 and x > 2.
  3. Check the result: The correct answer is x>2x>2.

A logarithm requires a positive argument, so x - 2 > 0 and x > 2.

5. QuestionMultiple choice

What is the vertical asymptote of f(x)=log⁡bxf(x)=\log_b x?

Please select an answer first.

Correct answer: A

The correct answer is x=0x=0.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: The logarithm's argument approaches zero from the right, creating the vertical asymptote x = 0.
  3. Check the result: The correct answer is x=0x=0.

The logarithm's argument approaches zero from the right, creating the vertical asymptote x = 0.

6. QuestionMultiple choice

What is the y-intercept of y=2xy=2^x?

Please select an answer first.

Correct answer: B

The correct answer is (0,1)(0,1).

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Substitute x = 0: y = 2^0 = 1, so the y-intercept is (0, 1).
  3. Check the result: The correct answer is (0,1)(0,1).

Substitute x = 0: y = 2^0 = 1, so the y-intercept is (0, 1).

7. QuestionMultiple choice

How is y=2x−3+1y=2^{x-3}+1 related to y=2xy=2^x?

Please select an answer first.

Correct answer: C

The correct answer is Shift right 3 units and up 1 unit..

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Replacing x with x - 3 shifts the graph right 3 units, and adding 1 shifts it up 1 unit.
  3. Check the result: The correct answer is Shift right 3 units and up 1 unit..

Replacing x with x - 3 shifts the graph right 3 units, and adding 1 shifts it up 1 unit.

8. QuestionMultiple choice

What happens as x increases for y=(13)xy=\left(\frac{1}{3}\right)^x?

Please select an answer first.

Correct answer: D

The correct answer is The function decreases..

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: An exponential function with a base between 0 and 1 represents decay, so it decreases as x increases.
  3. Check the result: The correct answer is The function decreases..

An exponential function with a base between 0 and 1 represents decay, so it decreases as x increases.

9. QuestionMultiple choice

What is the inverse function of y=10xy=10^x?

Please select an answer first.

Correct answer: A

The correct answer is y=log⁡10xy=\log_{10}x.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Exponential and logarithmic functions with the same base are inverses.
  3. Check the result: The correct answer is y=log⁡10xy=\log_{10}x.

Exponential and logarithmic functions with the same base are inverses.

10. QuestionMultiple choice

Solve log⁡2(x−1)=3\log_2(x-1)=3.

Please select an answer first.

Correct answer: B

The correct answer is x=9x=9.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Rewrite as 2^3 = x - 1, so 8 = x - 1 and x = 9.
  3. Check the result: The correct answer is x=9x=9.

Rewrite as 2^3 = x - 1, so 8 = x - 1 and x = 9.

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