Question

Solve for $x$:

$2^{2x+3}+2^5=2^6$.

Answer 1

Given,

$2^{2x+3}+2^5=2^6$

$\Rightarrow 2^{2x+3}=2^6-2^5$

$\Rightarrow 2^{2x+3}=2^5(2-1)$

$\Rightarrow 2^{2x+3}=2^5$

As the bases are same, equating the powers

$\Rightarrow 2x+3=5$

$\Rightarrow 2x=2$

$\Rightarrow x=1$.