Question

What value is equivalent to log base 2 13 to the nearest thousandth

Answer 1

To find the value of \(\log_2{13}\) to the nearest thousandth, we can use the change of base formula for logarithms:

\[
\log_b{a} = \frac{\log_k{a}}{\log_k{b}}
\]

We can use base 10 or base \(e\) (natural logarithm). Here, we will use base 10:

\[
\log_2{13} = \frac{\log_{10}{13}}{\log_{10}{2}}
\]

Using a calculator, we find:

- \(\log_{10}{13} \approx 1.113943\)
- \(\log_{10}{2} \approx 0.30103\)

Now substituting these values into the formula:

\[
\log_2{13} \approx \frac{1.113943}{0.30103} \approx 3.703
\]

Thus, the value of \(\log_2{13}\) to the nearest thousandth is:

\[
\boxed{3.703}
\]