If _ 10 x = y, then _ 1000 x^2 is equal to - Vidyadip

MCQ

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

A
${y^2}$
B
$2y$
C
${{3y} \over 2}$
✓
${{2y} \over 3}$

✓

Answer

Correct option: D.

${{2y} \over 3}$

d
(d) ${\log _{1000}}{x^2} = {\log _{{{10}^3}}}{x^2} = 2{\log _{{{10}^3}}}x = {2 \over 3}{\log _{10}}x = {2 \over 3}y$.

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