Question

Solve the following equation:
$4^{x-1}=2^x+8$

Answer 1

$4^{x-1}=2^x+8$

$\Rightarrow \frac{4^x}{4}=2^x+8$

$\Rightarrow 2^{2x}=4.2^x+32$

$\Rightarrow 2^{2x}-\mathrm{2.2.}{2}^x+4=32+4$

$\Rightarrow {(2^x-2)}^2=36$

$2^x-2=\sqrt{36}=\pm 6$

$2^x=8$ or $-4$

So, $x=3$ as $2^x\ne -4$

Answer $=3$