Question

Solve :

$2^3(5^0+3^{2x})=8\frac{8}{27}$

Answer 1

$\Rightarrow 2^3(5^0+3^{2x})=8\frac{8}{27}$

$\Rightarrow 2^3(1+3^{2x})=8+\frac{8}{27}$

$\Rightarrow 8(1+3^{2x})=8+\frac{8}{27}$

$\Rightarrow 8+8\times 3^{2x}=8+\frac{8}{27}$

$\Rightarrow 8\times 3^{2x}=\frac{8}{27}$

$\Rightarrow 3^{2x}=\frac{1}{27}$

$\Rightarrow 3^{2x}=3^{-3}$

As the bases are same, equating the powers

$2x=-3$

$x=-\frac{3}{2}$