📘 Precalculus Exponents And Logarithms

Recommended: 30–40 minutes. No calculator.

Problems

1.

Tags: Basic Exponent · Easy · source: Original (AMC-style)

What is 2³?

A) $4$ B) $6$ C) $8$ D) $9$ E) $12$

2.

Tags: Basic Logarithm · Easy · source: Original (AMC-style)

What is log₂(8)?

A) $2$ B) $3$ C) $4$ D) $8$ E) $16$

3.

Tags: Exponent Rules · Easy · source: Original (AMC-style)

What is 2² × 2³?

A) $2^5$ B) $2^6$ C) $4^5$ D) $4^6$ E) $8^5$

4.

Tags: Logarithm Rules · Easy · source: Original (AMC-style)

What is log₃(9) + log₃(3)?

A) $2$ B) $3$ C) $4$ D) $5$ E) $6$

5.

Tags: Negative Exponents · Easy · source: Original (AMC-style)

What is 2⁻²?

A) $-4$ B) $-2$ C) $\frac{1}{4}$ D) $\frac{1}{2}$ E) $4$

6.

Tags: Fractional Exponents · Easy · source: Original (AMC-style)

What is 4^(1/2)?

A) $2$ B) $4$ C) $8$ D) $16$ E) $32$

7.

Tags: Logarithm Properties · Medium · source: Original (AMC-style)

What is log₅(25) - log₅(5)?

A) $1$ B) $2$ C) $3$ D) $4$ E) $5$

8.

Tags: Exponential Equations · Medium · source: Original (AMC-style)

If 3ˣ = 27, what is x?

A) $2$ B) $3$ C) $4$ D) $5$ E) $6$

9.

Tags: Logarithmic Equations · Medium · source: Original (AMC-style)

If log₂(x) = 4, what is x?

A) $8$ B) $12$ C) $16$ D) $20$ E) $24$

10.

Tags: Change of Base · Medium · source: Original (AMC-style)

What is log₈(64)?

A) $1$ B) $2$ C) $3$ D) $4$ E) $8$

11.

Tags: Advanced Exponents · Hard · source: Original (AMC-style)

What is (2³)²?

A) $2^5$ B) $2^6$ C) $4^3$ D) $8^2$ E) $64$

12.

Tags: Complex Logarithms · Hard · source: Original (AMC-style)

What is log₂(3) + log₃(2)?

A) $1$ B) $2$ C) $\log_6(6)$ D) $\log_6(12)$ E) Cannot be simplified

Answer Key

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