If ${log}_{5} a . {log}_{a} x = 2$ , then value of $x$ is

125

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a^{2}

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25

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none of these

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Solution

The correct option is B $25$
${log}_{5} a {log}_{a} x = 2 \Rightarrow \frac{log a log x}{log 5 log a} = 2, [∵ {log}_{a} b = \frac{log b}{log a}] \Rightarrow log x = 2 log 5 = log 5^{2} \Rightarrow x = 25$
Ans: C

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{log}_{5} a . {log}_{a} x = 2,

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3 + {log}_{5} x = 2 {log}_{25} y

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