Question

Solve the following inequality:
$4^x-2^{2(x-1)}+8^{\frac{2(x-2)}{3}}>52$

Answer 1

$4^x-2^{2(x-1)}+8^{\frac{2(x-2)}{3}}>52$

${(2}^x{)}^2-{\left(\frac{2^x}{2}\right)}^2+{\left(\frac{2^x}{4}\right)}^2>52$

$let{2}^x=t$

$t^2+\frac{t^2}{16}-\frac{t^2}{4}>52$

$t^2(1+\frac{1}{16}-\frac{1}{4})-52>0$

$t^2\left(\frac{13}{16}\right)>52$

$t^2>64$

$t\epsilon (8,\infty )$

$2^x\epsilon (8,\infty )$

$x\epsilon (3,\infty )$