Question

Simplify:
$\log \left(\frac{x+y}{3}\right)=\frac{1}{2}\log x+\log \sqrt{y}$

Answer 1

Giventhat,

$\log \left(\frac{x+y}{3}\right)=\frac{1}{2}\log x+\log \sqrt{y}$

$\log \left(\frac{x+y}{3}\right)=\log \sqrt{x}+\log \sqrt{y}$ [From the property of $log$]

$\log \left(\frac{x+y}{3}\right)=\log (\sqrt{x}\times \sqrt{y})$ [From the property of $log$]

$\left(\frac{x+y}{3}\right)=(\sqrt{x}\times \sqrt{y})$

$x+y=3\times \sqrt{xy}$

$x^2+y^2+2xy=9xy$

$x^2+y^2-7xy=0$

Hence, this is the answer.