Question

Find the value of $x$
${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}={\left(\frac{5}{3}\right)}^{3x}$

Answer 1

${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}={\left(\frac{5}{3}\right)}^{3x}$

$\Rightarrow {\left(\frac{5}{3}\right)}^{-4-5}={\left(\frac{5}{3}\right)}^{3x}$ using $a^m\times a^n=a^{m+n}$

Since bases are same, we can equate the powers

$\Rightarrow 3x=-9$

$\Rightarrow x=\frac{-9}{3}=-3$

$\therefore x=-3$