Question

Solve for x:

$2^{3x+3}=2^{3x+1}+48$

Answer 1

As given$\Rightarrow 2^{3x+3}=2^{3x+1}+48$

$\Rightarrow 2^{3x+3}-2^{3x+1}=48$

$\Rightarrow 2^{3x}(2^3-2^1)=48$

$\Rightarrow 2^{3x}(8-2)=48$

$\Rightarrow 2^{3x}\left(6\right)=48$

$\Rightarrow 2^{3x}=\frac{48}{6}$

$\Rightarrow 2^{3x}=8$

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

Base are same so equating powers,

$3x=3$

$\therefore x=1$