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
0.259

Answer 1

To find \( \log 6 \) using the information given about \( \log 36 \), we can use the properties of logarithms.

We know that:
\[ 36 = 6^2 \]

Using the logarithmic identity \( \log a^b = b \cdot \log a \), we can express \( \log 36 \) as follows:
\[ \log 36 = \log(6^2) = 2 \cdot \log 6 \]

From the problem, we have:
\[ \log 36 \approx 1.556 \]

Thus, we can set up the equation:
\[ 2 \cdot \log 6 \approx 1.556 \]

Now, to solve for \( \log 6 \):
\[ \log 6 \approx \frac{1.556}{2} \]
\[ \log 6 \approx 0.778 \]

Therefore, to the nearest thousandth, \( \log 6 \) is approximately:
**0.778**