Precalculus Logarithms and Their Properties Quiz: 10 Questions with Explanations

A 5B 16C 6D 2.5

2^5 = 32, so the logarithm is 5.

A \(2^{4}=16\)B \(16^{2}=4\)C \(4^{2}=16\)D \(4^{16}=2\)

The base is 4 and the log 2 is the exponent.

A \(-3\)B \(3\)C \(-2\)D \(\frac{1}{3}\)

0.001 = 10^-3, so the logarithm is -3.

A \(\log_{b}(M+N)\)B \(\log_{b}M\cdot\log_{b}N\)C \(\frac{\log_{b}M}{\log_{b}N}\)D \(\log_{b}(MN)\)

The product rule says the sum of logs is the log of the product.

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

The y-axis, x = 0, is the vertical asymptote of every basic logarithm.

A \(2+2\log_{3}x\)B \(2\log_{3}9x\)C \(9+2\log_{3}x\)D \(2\log_{3}x\)

log3 9 = 2 and the power rule gives 2 log3 x. Dropping the 9 loses the 2.

A \(x>4\)B \(x>-4\)C \(x\ge-4\)D All real numbers

The argument x + 4 must be positive, so x > -4.

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

(3, 8) is on 2^x. The inverse swaps coordinates, giving (8, 3).

A 0B 1C 5D 25

A base raised to the first power equals itself, so log_b b = 1.

A 20B 100C 2D 10

The difference is 20 dB. Each 10 dB is a factor of 10, so 20 dB is 10 times 10 = 100.