KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 03 · Lesson 05

Exponential and Logarithmic Equations

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Exponential and Logarithmic Equations

U03 · L05
1

Rewrite log₂32=5 in exponential form.

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: 2⁵=32
Reasoning: A logarithm states the exponent.
2

Evaluate log₁₀0.001.

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: −3
Reasoning: 10^{-3}=0.001.
3

Expand ln(3x²).

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: ln3+2ln|x|
Reasoning: Use product and power properties.
4

Condense 2lnx−ln(x+1).

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: ln(x²/(x+1))
Reasoning: Use power and quotient properties.
5

Solve log₃(x−1)=2.

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: x=10
Reasoning: x−1=9.
6

Use change of base to express log₇20.

Logarithmic visualUse logarithms as inverse functions and exponents to solve equations, compare scales, and linearize multiplicative relationships. xy
Answer: ln20/ln7
Reasoning: Change-of-base formula.
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