Question
If log36≈1.556 , what is log6 to the nearest thousandth?(1 point)Responses0.7780.7781.2481.2480.2590.2590.519
Answers
GPT-4o mini
To find \( \log 6 \) using the given information \( \log 36 \approx 1.556 \), we can use the property of logarithms that relates the logarithm of a number and its square. Specifically, we know that:
\[
\log 36 = \log(6^2) = 2 \log 6
\]
From this equation, we can isolate \( \log 6 \):
\[
\log 6 = \frac{\log 36}{2}
\]
Now substituting the approximate value of \( \log 36 \):
\[
\log 6 = \frac{1.556}{2} \approx 0.778
\]
Thus, the value of \( \log 6 \) to the nearest thousandth is:
\[
\boxed{0.778}
\]
\[
\log 36 = \log(6^2) = 2 \log 6
\]
From this equation, we can isolate \( \log 6 \):
\[
\log 6 = \frac{\log 36}{2}
\]
Now substituting the approximate value of \( \log 36 \):
\[
\log 6 = \frac{1.556}{2} \approx 0.778
\]
Thus, the value of \( \log 6 \) to the nearest thousandth is:
\[
\boxed{0.778}
\]