Question

write the following logarithm in terms of the natural logarithm. then use a calculator to find the value of the logarithm, rounding your result to four decimal places. \\\\ \log_{2} 57 \\\\ write the logarithm in terms of the natural logarithm. \\\\ \log_{2} 57 = \square

Explanation:

Step1: Apply Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\ln a}{\ln b}$. For $\log_2 57$, we use this formula with $a = 57$ and $b = 2$. So, $\log_2 57=\frac{\ln 57}{\ln 2}$.

Step2: Calculate Natural Logarithms

First, find $\ln 57$ and $\ln 2$ using a calculator. $\ln 57\approx4.0431$, $\ln 2\approx0.6931$.

Step3: Divide the Results

Divide $\ln 57$ by $\ln 2$: $\frac{4.0431}{0.6931}\approx5.8332$.

Answer:

$\log_2 57 = \frac{\ln 57}{\ln 2}\approx5.8332$