Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 8 } ( 0.662 )$
A) $- 0.179$
B) -5.041
C) $- 0.198$
D) $12.085$

Question

Quizplus · Accepted Answer

The change of base formula allows us to convert $\log _ { 8 } ( 0.662 )$ into a more easily calculable form, such as $\frac{\log(0.662)}{\log(8)}$ or $\frac{\ln(0.662)}{\ln(8)}$, using either base 10 (log) or base e (ln) logarithms. Using a calculator to evaluate either form gives a result close to $-0.198$, making option C the correct answer.

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Use a Change of Base Formula to Evaluate the Given $\log _ { 8 } ( 0.662 )$