Question

If log36≈1.556
, what is log6
to the nearest thousandth?(1 point)
Responses

1.248
1.248

0.778
0.778

0.519
0.519

0.259

Answer 1

To find \(\log 6\) given that \(\log 36 \approx 1.556\), we can use the property of logarithms that states:

\[
\log a^b = b \cdot \log a
\]

Since \(36\) can be expressed as \(6^2\), we can rewrite \(\log 36\) as:

\[
\log 36 = \log (6^2) = 2 \cdot \log 6
\]

Given that:

\[
\log 36 \approx 1.556
\]

we can set up the equation:

\[
2 \cdot \log 6 \approx 1.556
\]

Now, solve for \(\log 6\):

\[
\log 6 \approx \frac{1.556}{2} \approx 0.778
\]

Therefore, \(\log 6\) to the nearest thousandth is:

\[
\boxed{0.778}
\]