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Fundamental Laws of Logarithms

If log10 x=y ...

Question

If $l o g_{10} x = y t h e n l o g_{1000} x^{2}$ is equal to

A

y^{2}

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B

2 y

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C

\frac{3 y}{2}

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D

\frac{2 y}{3}

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Solution

The correct option is D $\frac{2 y}{3}$
$l o g_{1000} x^{2}$
$= l o g_{10^{3}} x^{2}$
$= 2 l o g_{10^{3}} x$
$= \frac{2}{3} l o g_{10} x$
$= \frac{2}{3} y$

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