Algebra 2 Logarithms Quiz: 10 Questions with Explanations

A 3B 4C 16D 2

2 raised to the 3rd power is 8, so the log base 2 of 8 is 3.

A \(2^{5} = 25\)B \(5^{2} = 25\)C \(25^{2} = 5\)D \(5^{25} = 2\)

The base 5 is raised to the exponent 2 to give 25.

A 2B -2C -0.01D 0.1

0.01 = 10^(-2), so the common log is -2.

A \(y = 0\)B \(x = 1\)C \(y = 1\)D \(x = 0\)

A logarithm is undefined for x ≤ 0, and the graph approaches the y-axis, so the asymptote is x = 0.

A \(\log 2 \cdot \log 3\)B \(\log 3 – \log 2\)C \(\log 2 + \log 3\)D \(2\log 3\)

The product rule: log(2 · 3) = log 2 + log 3.

A 7B 4C 28D 1

A logarithm and its base cancel: log_b(b^n) = n.

A \(x = 16\)B \(x = 5\)C \(x = 6\)D \(x = 30\)

2^5 = 32, or x = log2 32 = 5.

A \((3, 8)\)B \((-3, 8)\)C \((8, 3)\)D \((8, -3)\)

Inverse functions swap coordinates, so (8, 3) is on the log graph.

A 2.73B 6.67C 0.37D 1.30

ln 20 / ln 3 = 2.9957 / 1.0986 is about 2.73.

A log4(16) = 4 because 16 ÷ 4 = 4B log4(1) = 1 because 4 ÷ 4 = 1C log4(1/4) = 1 because 1/4 is 4 invertedD log4(16) = 2 because 4² = 16

The log is the exponent: 4 to the 2 is 16. Also log4(1) = 0 because 4 to the 0 is 1.