Question

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

Answer 1

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

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

$\Rightarrow {\left(\frac{5}{3}\right)}^{-9}={\left(\frac{5}{3}\right)}^{3x}$

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

Hence x =-3