Use a calculator and the change-of-base formula to find the logarithm to four decimal places.
-$\log _{6} 0.899$
A) -16.8284
B) -0.0462
C) 6.6741
D) -0.0594

Question

Quizplus · Accepted Answer

The change-of-base formula allows us to convert the given logarithm to a base that our calculator can handle, typically base 10 or base e (natural logarithm). The formula is $\log_b a = \frac{\log_k a}{\log_k b}$, where $k$ is a new base, and $a$ and $b$ are the numbers in the original logarithm. Using a calculator with base 10, we find $\log_{6} 0.899 = \frac{\log 0.899}{\log 6} \approx -0.0594$.

Use a Calculator and the Change-Of-Base Formula to Find the Logarithm