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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

Evaluate log⁡28\log_2 8.

Please select an answer first.

Correct answer: A

The correct answer is 3.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Because 2^3 = 8, log base 2 of 8 is 3.
  3. Check the result: The correct answer is 3.

Because 2^3 = 8, log base 2 of 8 is 3.

2. QuestionMultiple choice

Evaluate log⁡51\log_5 1.

Please select an answer first.

Correct answer: B

The correct answer is 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: Every positive base raised to the zero power equals 1, so log base 5 of 1 is 0.
  3. Check the result: The correct answer is 0.

Every positive base raised to the zero power equals 1, so log base 5 of 1 is 0.

3. QuestionMultiple choice

Evaluate log⁡(0.01)\log(0.01).

Please select an answer first.

Correct answer: C

The correct answer is -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: The common logarithm asks for the exponent on 10: 10^(-2) = 0.01.
  3. Check the result: The correct answer is -2.

The common logarithm asks for the exponent on 10: 10^(-2) = 0.01.

4. QuestionMultiple choice

Evaluate ln⁡(e4)\ln(e^4).

Please select an answer first.

Correct answer: D

The correct answer is 4.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Natural logarithm and the exponential function with base e are inverse functions.
  3. Check the result: The correct answer is 4.

Natural logarithm and the exponential function with base e are inverse functions.

5. QuestionMultiple choice

Evaluate log⁡3(19)\log_3\left(\frac{1}{9}\right).

Please select an answer first.

Correct answer: A

The correct answer is -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: Since 1/9 = 3^(-2), the logarithm equals -2.
  3. Check the result: The correct answer is -2.

Since 1/9 = 3^(-2), the logarithm equals -2.

6. QuestionMultiple choice

Rewrite log⁡216=4\log_2 16=4 in exponential form.

Please select an answer first.

Correct answer: B

The correct answer is 24=162^4=16.

  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 equation log base b of x = y is equivalent to b^y = x.
  3. Check the result: The correct answer is 24=162^4=16.

The equation log base b of x = y is equivalent to b^y = x.

7. QuestionMultiple choice

If log⁡bx=y\log_b x=y, which equation is equivalent?

Please select an answer first.

Correct answer: C

The correct answer is by=xb^y=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: The logarithm definition states that the base raised to the logarithm equals the argument.
  3. Check the result: The correct answer is by=xb^y=x.

The logarithm definition states that the base raised to the logarithm equals the argument.

8. QuestionMultiple choice

Evaluate log⁡(1000)\log(1000).

Please select an answer first.

Correct answer: D

The correct answer is 3.

  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 common logarithm is 3 because 10^3 = 1000.
  3. Check the result: The correct answer is 3.

The common logarithm is 3 because 10^3 = 1000.

9. QuestionMultiple choice

Evaluate log⁡42\log_4 2.

Please select an answer first.

Correct answer: A

The correct answer is 12\frac{1}{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: Because 4^(1/2) = 2, log base 4 of 2 is 1/2.
  3. Check the result: The correct answer is 12\frac{1}{2}.

Because 4^(1/2) = 2, log base 4 of 2 is 1/2.

10. QuestionMultiple choice

Evaluate ln⁡1\ln 1.

Please select an answer first.

Correct answer: B

The correct answer is 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 natural logarithm of 1 is 0 because e^0 = 1.
  3. Check the result: The correct answer is 0.

The natural logarithm of 1 is 0 because e^0 = 1.

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