Question

Given that $y=4\times {10}^{2x}$, Write $x$ in terms of $y$, using logarithmic base 10

• A. $x=lo{g}_{10}\frac{y}{4}$
• B. $x=\frac{1}{2}lo{g}_{10}\frac{y}{4}$
• C. $x=\frac{1}{4}lo{g}_{10}\frac{y}{4}$
• D. $x=\frac{1}{4}lo{g}_{10}\frac{y}{4}$

Answer 1

The correct option is B $x=\frac{1}{2}lo{g}_{10}\frac{y}{4}$

$y=4\times {10}^{2x}$
$y/4={10}^{2x}$
We know,
If $y=a^x$, then $x=lo{g}_{a}y$
So, $2x=lo{g}_{10}\frac{y}{4}$
$x=\frac{1}{2}lo{g}_{10}\frac{y}{4}$