Question
The value of $${\log _5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}}$$ is equal to -
Answer: Option B
$$\eqalign{
& {\text{lo}}{{\text{g}}_5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}} \cr
& = {\text{lo}}{{\text{g}}_5}\left( {\frac{{{5^3} \times {5^4}}}{{{5^2}}}} \right) \cr
& = {\text{lo}}{{\text{g}}_5}{5^5} \cr
& {\text{ = 5lo}}{{\text{g}}_5}5 \cr
& = 5 \cr} $$
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$$\eqalign{
& {\text{lo}}{{\text{g}}_5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}} \cr
& = {\text{lo}}{{\text{g}}_5}\left( {\frac{{{5^3} \times {5^4}}}{{{5^2}}}} \right) \cr
& = {\text{lo}}{{\text{g}}_5}{5^5} \cr
& {\text{ = 5lo}}{{\text{g}}_5}5 \cr
& = 5 \cr} $$
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