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If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

A. 2.870

B. 2.967

C. 3.876

D. 3.912

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\log _5}512 \cr & = {{\log 512} \over {\log 5}} \cr & = {{\log {2^9}} \over {\log \left( {{{10} \over 2}} \right)}} \cr & = {{9\log 2} \over {\log 10 - \log 2}} \cr & = {{\left( {9 \times 0.3010} \right)} \over {1 - 0.3010}} \cr & = {{2.709} \over {0.699}} \cr & = {{2709} \over {699}} \cr & = 3.876 \cr} $$

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