Question

question 7 of 10
evaluate the following expression. round your answer to two decimal places.
\\(\log_{6} e\\)
\\(\bigcirc\\) a. 0.43
\\(\bigcirc\\) b. 0.56
\\(\bigcirc\\) c. 1.38
\\(\bigcirc\\) d. 1.79

Explanation:

Step1: Recall Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\ln a}{\ln b}$ (or $\frac{\log a}{\log b}$ with any base). For $\log_6 e$, we use this formula: $\log_6 e = \frac{\ln e}{\ln 6}$.

Step2: Simplify and Calculate

We know $\ln e = 1$, so we need to calculate $\frac{1}{\ln 6}$. First, find $\ln 6 \approx 1.7918$. Then, $\frac{1}{1.7918} \approx 0.558 \approx 0.56$ when rounded to two decimal places.

Answer:

B. 0.56