Question

What value is equivalent to log243
to the nearest thousandth? Use the change of base formula to determine your answer.(1 point)
Responses

0.817
0.817

1.332
1.332

0.184
0.184

5.426

Answer 1

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:

1. \(\log_{10}(43) \approx 1.633\)
2. \(\log_{10}(2) \approx 0.301\)

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**.