To find the value of \(\log_{2}(43)\) using the change of base formula, you can use:
\[ \log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)} \]
Where \(k\) can be any base, commonly base 10 or base \(e\). Here, we will use base 10.
Thus, we can calculate:
\[ \log_{2}(43) = \frac{\log_{10}(43)}{\log_{10}(2)} \]
Using a calculator to find these logarithmic values:
- \(\log_{10}(43) \approx 1.633\)
- \(\log_{10}(2) \approx 0.301\)
Now, substitute these values into the formula:
\[ \log_{2}(43) \approx \frac{1.633}{0.301} \approx 5.426 \]
Therefore, the value of \(\log_{2}(43)\) to the nearest thousandth is 5.426.