Question

The values of $x$ satisfying the equation $4^x-5\left(2^x\right)+4=0$ are

• A. $0,2$
• B. $0,-2$
• C. $2,-2$
• D. None of these

Answer 1

The correct option is A $0,2$

Given equation is $4^x-5\left(2^x\right)+4=0$

$\therefore {\left(2^x\right)}^2-5\left(2^x\right)+4=0$
Let $2^x=y$
$\Rightarrow y^2-5y+4=0$
$\Rightarrow (y-1)(y-4)=0$
$\Rightarrow y=1,4$
$\Rightarrow 2^x=1;2^x=4$
$\Rightarrow 2^x=2^0;2^x=2^2$
$\Rightarrow x=0,x=2$