If $\log_{2} = 0 .3010$ and $\log_{3} = 0 .4771$ the value of $\log_{5} 512$ is ___

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2.870

3.912

3.876

2.967

answer is C.

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Detailed Solution

$\frac{\log 512}{\log 5} = \frac{\log 2^{9}}{\log (\frac{10}{2})} = \frac{9 \log 2}{\log 10 - \log 2} = \frac{9 (0 .3010)}{1 - 0 .3010} = \frac{2 .709}{0 .699} = \frac{2709}{699} = 3 .876$

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