Question

Question
What value is equivalent to log42.1
to the nearest thousandth? Use the change of base formula to determine your answer.(1 point)
Responses

0.535
0.535

1.868
1.868

0.287
0.287

0.081

Answer 1

To calculate \( \log_4{2.1} \) using the change of base formula, you can use the formula:

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

where \( k \) can be any positive number (commonly base 10 or base e).

Using base 10, we have:

\[
\log_4{2.1} = \frac{\log_{10}{2.1}}{\log_{10}{4}}
\]

Now we can calculate each log value using a calculator:

- \( \log_{10}{2.1} \approx 0.3222 \)
- \( \log_{10}{4} \approx 0.6021 \)

Now, we can substitute these values into the change of base formula:

\[
\log_4{2.1} = \frac{0.3222}{0.6021} \approx 0.535
\]

Rounding to the nearest thousandth gives us \( 0.535 \).

Therefore, the correct response is:

**0.535**