If $l o g_{5} a . l o g_{a} x = 2$ , then $x$ is equal to:

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 C $25$
$l o g_{5} a . l o g_{a} x = 2$
$= \frac{l o g a}{l o g 5} . \frac{l o g x}{l o g a} = 2$
$= l o_{5} x = 2$
$x = 5^{2}$
$x = 25$

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