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The value of $${\log _5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}}$$    is equal to -

A. 725

B. 5

C. 3125

D. 6

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{lo}}{{\text{g}}_5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}} \cr & = {\text{lo}}{{\text{g}}_5}\left( {\frac{{{5^3} \times {5^4}}}{{{5^2}}}} \right) \cr & = {\text{lo}}{{\text{g}}_5}{5^5} \cr & {\text{ = 5lo}}{{\text{g}}_5}5 \cr & = 5 \cr} $$

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