Question

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

0.778
0.778

0.519
0.519

1.248
1.248

0.259

Answer 1

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

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

We know that \( 36 = 6^2 \), so we can write:

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

Given that \( \log 36 \approx 1.556 \), we can set up the equation:

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

To solve for \( \log 6 \), we divide both sides by 2:

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

Thus, \( \log 6 \) to the nearest thousandth is \( 0.778 \).

Final answer:

**0.778**