Question

Given that $y=4\times {10}^{2x}$, express $x$ in terms of $y$, giving an exact simplified answer in terms of logarithmic base $10$.

• A. $x=\frac{1}{4}{\log }_{10}\left(y/2\right)$
• B. $x=\frac{1}{2}{\log }_{10}\left(y/2\right)$
• C. $x=\frac{1}{2}{\log }_{10}\left(y/4\right)$
• D. None of the above

Answer 1

The correct option is C $x=\frac{1}{2}{\log }_{10}\left(y/4\right)$

$y=4\times {10}^{2x}$
$y/4={10}^{2x}$
We know, if $y=a^x$, then $x={\log }_{a}y$

So, $2x={\log }_{10}\left(y/4\right)$
$x=\frac{1}{2}{\log }_{10}\left(y/4\right)$