${log}_{5} 625 + {log}_{3} 243 + {log}_{7} 343$

3

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5

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9

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12

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Solution

The correct option is B $12$
${log}_{5} 625 + {log}_{3} 243 + {log}_{7} 343$
$= {log}_{5} 5^{4} + {log}_{3} 3^{5} + {log}_{7} 7^{3}$
$= 4 {log}_{5} 5 + 5 {log}_{3} 3 + 3 {log}_{7} 7$ [ $∵ {log}_{a} b^{n} = n {log}_{a} b$ ]
$= 4 + 5 + 3$ [ $∵ {log}_{a} a = 1$ ]
$= 12$

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