Question

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

• A. $y^2$
• B. $2y$
• C. $\frac{3y}{2}$
• D. $\frac{2y}{3}$

Answer 1

The correct option is D $\frac{2y}{3}$

$lo{g}_{1000}{x}^2$
$=lo{g}_{{10}^3}{x}^2$
$=2lo{g}_{{10}^3}x$
$=\frac{2}{3}lo{g}_{10}x$
$=\frac{2}{3}y$