Question

score on last try: 0 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. jump to last sub > next question get a similar question you can retry this question below use the change of base formula to rewrite the logarithm in terms of the natural logarithm: \\(\log_{6}(27) = \\) use a calculator to evaluate the logarithm. round to four decimal places.

Explanation:

Step1: Recall Change of Base Formula

The change of base formula for a logarithm $\log_b(a)$ is $\frac{\ln(a)}{\ln(b)}$ when rewriting in terms of natural logarithms ($\ln$). For $\log_{6}(27)$, we apply this formula.
$\log_{6}(27)=\frac{\ln(27)}{\ln(6)}$

Step2: Evaluate the Expression

First, calculate $\ln(27)$ and $\ln(6)$ using a calculator. $\ln(27)\approx3.2958$, $\ln(6)\approx1.7918$. Then divide them: $\frac{3.2958}{1.7918}\approx1.8394$.

Answer:

First part: $\frac{\ln(27)}{\ln(6)}$
Second part: $1.8394$