Question
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
Answer: Option C
$$\eqalign{
& {\log _5}512 \cr
& = {{\log 512} \over {\log 5}} \cr
& = {{\log {2^9}} \over {\log \left( {{{10} \over 2}} \right)}} \cr
& = {{9\log 2} \over {\log 10 - \log 2}} \cr
& = {{ {9 \times 0.3010} } \over {1 - 0.3010}} \cr
& = {{2.709} \over {0.699}} \cr
& = {{2709} \over {699}} \cr
& = 3.876 \cr} $$
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$$\eqalign{
& {\log _5}512 \cr
& = {{\log 512} \over {\log 5}} \cr
& = {{\log {2^9}} \over {\log \left( {{{10} \over 2}} \right)}} \cr
& = {{9\log 2} \over {\log 10 - \log 2}} \cr
& = {{ {9 \times 0.3010} } \over {1 - 0.3010}} \cr
& = {{2.709} \over {0.699}} \cr
& = {{2709} \over {699}} \cr
& = 3.876 \cr} $$
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