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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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1. Test

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

Simplify x3⋅x4x^3\cdot x^4.

Please select an answer first.

Correct answer: A

The correct answer is x7x^7.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: When multiplying powers with the same base, add the exponents: x^3 · x^4 = x^(3+4) = x^7.
  3. Check the result: The correct answer is x7x^7.

When multiplying powers with the same base, add the exponents: x^3 · x^4 = x^(3+4) = x^7.

2. QuestionMultiple choice

Simplify a5a2\frac{a^5}{a^2} for a≠0a\ne0.

Please select an answer first.

Correct answer: B

The correct answer is a3a^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: When dividing powers with the same nonzero base, subtract the exponents: a^(5-2) = a^3.
  3. Check the result: The correct answer is a3a^3.

When dividing powers with the same nonzero base, subtract the exponents: a^(5-2) = a^3.

3. QuestionMultiple choice

Simplify (2x3)2(2x^3)^2.

Please select an answer first.

Correct answer: C

The correct answer is 4x64x^6.

  1. Identify the exponential or logarithmic structure: Determine the base, exponent, logarithm, growth factor, decay factor, or graph feature involved.
  2. Apply the relationship: Square the coefficient and multiply the exponent by 2: 2^2(x^3)^2 = 4x^6.
  3. Check the result: The correct answer is 4x64x^6.

Square the coefficient and multiply the exponent by 2: 2^2(x^3)^2 = 4x^6.

4. QuestionMultiple choice

Evaluate 2−32^{-3}.

Please select an answer first.

Correct answer: D

The correct answer is 18\frac{1}{8}.

  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 negative exponent means a reciprocal: 2^(-3) = 1/(2^3) = 1/8.
  3. Check the result: The correct answer is 18\frac{1}{8}.

A negative exponent means a reciprocal: 2^(-3) = 1/(2^3) = 1/8.

5. QuestionMultiple choice

Simplify (x2y3)(x4y)(x^2y^3)(x^4y).

Please select an answer first.

Correct answer: A

The correct answer is x6y4x^6y^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: Add exponents for each common base: x^(2+4)y^(3+1) = x^6y^4.
  3. Check the result: The correct answer is x6y4x^6y^4.

Add exponents for each common base: x^(2+4)y^(3+1) = x^6y^4.

6. QuestionMultiple choice

For x≠0x\ne0, what is x0x^0?

Please select an answer first.

Correct answer: B

The correct answer is 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: Any nonzero base raised to the zero power equals 1.
  3. Check the result: The correct answer is 1.

Any nonzero base raised to the zero power equals 1.

7. QuestionMultiple choice

Simplify 32⋅343^2\cdot3^4.

Please select an answer first.

Correct answer: C

The correct answer is 363^6.

  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 bases match, so add exponents: 3^(2+4) = 3^6.
  3. Check the result: The correct answer is 363^6.

The bases match, so add exponents: 3^(2+4) = 3^6.

8. QuestionMultiple choice

Evaluate (12)−2\left(\frac{1}{2}\right)^{-2}.

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: Invert the base and use the positive exponent: (1/2)^(-2) = 2^2 = 4.
  3. Check the result: The correct answer is 4.

Invert the base and use the positive exponent: (1/2)^(-2) = 2^2 = 4.

9. QuestionMultiple choice

Evaluate 10010^0.

Please select an answer first.

Correct answer: A

The correct answer is 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: The zero-exponent rule gives 10^0 = 1 because 10 is nonzero.
  3. Check the result: The correct answer is 1.

The zero-exponent rule gives 10^0 = 1 because 10 is nonzero.

10. QuestionMultiple choice

Simplify (m2n)3(m^2n)^3.

Please select an answer first.

Correct answer: B

The correct answer is m6n3m^6n^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: Apply the power of a product rule: (m^2n)^3 = m^(2·3)n^3 = m^6n^3.
  3. Check the result: The correct answer is m6n3m^6n^3.

Apply the power of a product rule: (m^2n)^3 = m^(2·3)n^3 = m^6n^3.

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