Precalculus Exponential and Logarithmic Equations Quiz: 10 Questions with Explanations

A 8B 2C 4D 14

16 = 2^4, so x = 4. Dividing 16 by 2 would give 8, which is not the exponent.

A \(\frac{\ln5}{\ln40}\)B \(\ln40-\ln5\)C \(\frac{\ln40}{\ln5}\)D \(\frac{40}{5}\)

Take ln of both sides: x ln 5 = ln 40, so x = ln 40 / ln 5.

A 9B 7C 8D 5

x – 1 = 2^3 = 8, so x = 9. Forgetting to add the 1 gives 8.

A \(7e\)B \(\ln7\)C \(\frac{7}{e}\)D \(\log_{7}e\)

Take ln of both sides: x = ln 7.

A 3.32B 5C 2.32D 10

The curve meets the line near x = 3.32 = log base 2 of 10.

A Only -2B Only 5C BothD Neither

-2 makes log(-2) undefined, so it is extraneous. The graph exists only for x > 3.

A \(\frac{2}{r}\)B \(r\ln2\)C \(\frac{r}{\ln2}\)D \(\frac{\ln2}{r}\)

Solve e^(rt) = 2 to get t = ln 2 / r.

A \(x(x+6)=27\)B \(x+x+6=9\)C \(x(x+6)=9\)D \(2x+6=27\)

Combine to log3 of x(x + 6) = 3, then x(x + 6) = 3^3 = 27.

A 2B 3C 1.5D 6

4^x = 2^(2x), so 2x = x + 3 and x = 3.

A 10 yearsB 20 yearsC 7.1 yearsD 14.2 years

1.05^t = 2 gives t = ln 2 / ln 1.05, about 14.2. The rule of 72 gives about 14.4.