Question

question 10 of 10
evaluate the following expression. round your answer to two decimal places.
\\(\log_{6} 8\\)
\\(\bigcirc\\) a. 2.08
\\(\bigcirc\\) b. 0.86
\\(\bigcirc\\) c. 1.16
\\(\bigcirc\\) d. 0.90

Explanation:

Step1: Use Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\log_c a}{\log_c b}$ (we can use $c = 10$ or $c = e$). Here, $b = 6$ and $a = 8$, so $\log_6 8=\frac{\log 8}{\log 6}$.

Step2: Calculate Logarithms

Using a calculator, $\log 8\approx0.9031$ and $\log 6\approx0.7782$. Then $\frac{0.9031}{0.7782}\approx1.16$.

Answer:

C. 1.16