Question

If ${\log }_{10}x=a$ and ${\log }_{10}y=b$, then ${10}^{2b}$ in terms of $y$ is equal to

• A. $y$
• B. $y^2$
• C. $y^3$
• D. $y^4$

Answer 1

The correct option is B $y^2$

Given, ${\log }_{10}x=a,{\log }_{10}y=b$

$\Rightarrow {10}^b=y$

Consider, ${10}^{2b}$

$={10}^{b+b}$

$={10}^b{.10}^b$

$=y.y$

$=y^2$.