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Fundamental Laws of Logarithms

If 3+log 5 x ...

Question

If $3 + {log}_{5} x = 2 {log}_{25} y$ , then the value of $x$ is

A

\frac{y}{25}

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B

\frac{2 y}{125}

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C

\frac{y}{75}

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D

\frac{y}{125}

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Solution

The correct option is D $\frac{y}{125}$
$3 + {log}_{5} x = 2 {log}_{25} y \Rightarrow 3 {log}_{5} 5 + {log}_{5} x = 2 {log}_{25} y \Rightarrow 125 x = y \Rightarrow x = \frac{y}{125}$

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Fundamental Laws of Logarithms

Standard XI Mathematics

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