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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

Solve 2x=162^x=16.

Please select an answer first.

Correct answer: A

The correct answer is x=4x=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: Since 16 = 2^4, equal bases give x = 4.
  3. Check the result: The correct answer is x=4x=4.

Since 16 = 2^4, equal bases give x = 4.

2. QuestionMultiple choice

Solve 3x+1=273^{x+1}=27.

Please select an answer first.

Correct answer: B

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: Rewrite 27 as 3^3, so x + 1 = 3 and x = 2.
  3. Check the result: The correct answer is x=2x=2.

Rewrite 27 as 3^3, so x + 1 = 3 and x = 2.

3. QuestionMultiple choice

Solve 52x=1255^{2x}=125.

Please select an answer first.

Correct answer: C

The correct answer is x=32x=\frac{3}{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: Rewrite 125 as 5^3: 2x = 3, so x = 3/2.
  3. Check the result: The correct answer is x=32x=\frac{3}{2}.

Rewrite 125 as 5^3: 2x = 3, so x = 3/2.

4. QuestionMultiple choice

Solve 4x=84^x=8.

Please select an answer first.

Correct answer: D

The correct answer is x=32x=\frac{3}{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: Write 4^x as 2^(2x) and 8 as 2^3. Then 2x = 3, so x = 3/2.
  3. Check the result: The correct answer is x=32x=\frac{3}{2}.

Write 4^x as 2^(2x) and 8 as 2^3. Then 2x = 3, so x = 3/2.

5. QuestionMultiple choice

Solve 10x=0.00110^x=0.001.

Please select an answer first.

Correct answer: A

The correct answer is x=−3x=-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 0.001 = 10^(-3), x = -3.
  3. Check the result: The correct answer is x=−3x=-3.

Because 0.001 = 10^(-3), x = -3.

6. QuestionMultiple choice

Solve 2x−1=82^{x-1}=8.

Please select an answer first.

Correct answer: B

The correct answer is x=4x=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: Rewrite 8 as 2^3, so x - 1 = 3 and x = 4.
  3. Check the result: The correct answer is x=4x=4.

Rewrite 8 as 2^3, so x - 1 = 3 and x = 4.

7. QuestionMultiple choice

Solve 9x=279^x=27.

Please select an answer first.

Correct answer: C

The correct answer is x=32x=\frac{3}{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: Write 9^x as 3^(2x) and 27 as 3^3, giving 2x = 3 and x = 3/2.
  3. Check the result: The correct answer is x=32x=\frac{3}{2}.

Write 9^x as 3^(2x) and 27 as 3^3, giving 2x = 3 and x = 3/2.

8. QuestionMultiple choice

Solve 7x+2=17^{x+2}=1.

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 positive base other than 1 equals 1 only when its exponent is zero, so x + 2 = 0.
  3. Check the result: The correct answer is x=−2x=-2.

A positive base other than 1 equals 1 only when its exponent is zero, so x + 2 = 0.

9. QuestionMultiple choice

Solve 4x=1164^x=\frac{1}{16}.

Please select an answer first.

Correct answer: A

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: Since 1/16 = 4^(-2), x = -2.
  3. Check the result: The correct answer is x=−2x=-2.

Since 1/16 = 4^(-2), x = -2.

10. QuestionMultiple choice

Solve ex=e5e^x=e^5.

Please select an answer first.

Correct answer: B

The correct answer is x=5x=5.

  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 exponential function with base e is one-to-one, so equal outputs require x = 5.
  3. Check the result: The correct answer is x=5x=5.

The exponential function with base e is one-to-one, so equal outputs require x = 5.

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