Question

What are the roots of the equation $4^x-{3.2}^{x+2}+32=0$?

• A. $1,2$
• B. $3,4$
• C. $2,3$
• D. $1,3$

Answer 1

The correct option is C $2,3$

Given equation is $4^x-{3.2}^{x+2}+32=0$
Put $2^x=t$
$\Rightarrow t^2-3.t\times 4+32=0$
$\Rightarrow t^2-12t+32=0$

$\Rightarrow t^2-8t-4t+32=0$

$\Rightarrow (t-8)(t-4)=0$
$\Rightarrow t=4,8$

Resubstitute value of $t$, we get

$2^x=4=2^2$ and $2^x=8=2^3$

Therefore, $x=2,3$