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Logarithms

If log5 x =...

Question

If ${log}_{5} x = y$ and $5^{2 y + 3}$ = $m x^{2}$ , then the value of $m$ is equal to

100

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125

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70

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150

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Solution

The correct option is B $125$
${log}_{5} x = y$ ....(Given)
$∴ x = 5^{y}$ .....(1)
$5^{2 y + 3} = 5^{2 y} \times 5^{3} = (5^{y})^{2} \times 125$
= $125 x^{2}$ ....(From 1)

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