Question

Solve: $2^{2+x}+2^{x+2}-4\times 2^3=0$

Answer 1

Given equation is
$\Rightarrow 2^{2+x}+2^{x+2}-4\times 2^3=0$
$\Rightarrow 2^{2+x}+2^{x+2}-4\times 8=0$
$\Rightarrow 2^{2+x}+2^{x+2}=32$
$\Rightarrow 2^x(2^2+2^2)=32$
$\Rightarrow 2^x(4+4)=32$
$\Rightarrow 2^x=\frac{32}{8}$
$\Rightarrow 2^x=4$
$\Rightarrow 2^x=2^2$
Base are same so equate the powers,
$\Rightarrow x=2$