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Q.

If $\log_{10} x = y,$ then $\log_{1000} x^{2}$ is equal to

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a

$\frac{3 y}{2}$

b

$2 y$

c

$y^{2}$

d

$\frac{2 y}{3}$

answer is D.

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Detailed Solution

$\log_{1000} x^{2} = \log_{10^{3}} x^{2} = 2 \log_{10^{3}} x = \frac{2}{3} \log_{10} x = \frac{2}{3} y .$

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