Question

Solve: $2^{2x}+2^{x+1}=4-2^x$

• A. $x=2$
• B. $x=1$
• C. $x=0$
• D. None of these

Answer 1

The correct option is C $x=0$

Given equation is: $2^{2x}+2^{x+1}=4-2^x$
$\Rightarrow 2^{2x}+2^x.2=4-2^x$
$\Rightarrow 2^{2x}+{3.2}^x-4=0$
Let, $2^x=y$
$\Rightarrow y^2+3y-4=0$
$\Rightarrow (y+4)(y-1)=0$
$\Rightarrow y=-4y=1$
$\Rightarrow 2^x=-42^x=1$
$\Rightarrow 2^x=2^0$
$\Rightarrow x=0$