Question

If $a^2+b^2=23ab$, show that:
$\log \frac{a+b}{5}=\frac{1}{2}(\log a+\log b)$.

Answer 1

$a^2+b^2=23ab$

or,$a^2+b^2+2ab=25ab$

or, $(a+b{)}^2=25ab$

or, $(a+b)=5\sqrt{ab}$

or, $\frac{a+b}{5}=\sqrt{ab}$

$\Rightarrow \log \frac{a+b}{5}=\frac{1}{2}\log \left(ab\right)$

or, $\log \frac{a+b}{5}=\frac{1}{2}(\log a+\log b)$