Question

Solve the following equation:
$4^x-10.2^{x-1}=24$

Answer 1

Let $2^x$ be $t,t>0$

$4^x-{10.2}^{x-1}=24$

$t^2-5t-24=0$

$(t-8)(t+3)=0$

$t=8$or $-3$

$t=8$

$2^x=8$

$2^x=2^3$

$x=3$