If $\log 2 = 0.3010$ and $\log 3 = 0.4771$ , the value of $\log_{5} 512$ is

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3.876

3.912

2.967

2.870.

answer is C.

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Detailed Solution

$\begin{array}{l} \log_{5} 512 = \frac{\log 512}{\log 5} \\ = \frac{\log 2^{9}}{\log (10 / 2)} \\ = \frac{9 \log 2}{\log 10 - \log 2} \\ = \frac{(9 \times 0.3010)}{1 - 0.3010} \\ = \frac{2.709}{0.699} \\ = 3.876 \end{array}$

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