Question

If log341≈3.38
and log32≈0.631
, what is log382
, to the nearest thousandth?

Answer 1

To find \( \log_3 82 \) using the given values of \( \log_3 41 \approx 3.38 \) and \( \log_3 2 \approx 0.631 \), we can use the logarithm properties.

We note that:

\[
\log_3 82 = \log_3 (41 \times 2) = \log_3 41 + \log_3 2
\]

Using the values provided:

\[
\log_3 82 \approx 3.38 + 0.631
\]

Now, we perform the addition:

\[
3.38 + 0.631 = 4.011
\]

Thus, rounding to the nearest thousandth, we have:

\[
\log_3 82 \approx 4.011
\]

Therefore, the answer is:

\[
\boxed{4.011}
\]