Question

The solution of the equation $4^x+2^x=6$ is/are

• A. $0,1$
• B. $2,1$
• C. $1,0$
• D. $1$

Answer 1

Answer: (D)

$1$

Given,
$4^x+2^x=6$
$=2^{2x}+2^x-6=0$
$=(2^x{)}^2+2^x-6=0$
Now put $2^x=y$
$\Rightarrow y^2+y-6=0$
$\Rightarrow y^2+3y-2y-6=0$
$\Rightarrow y(y+3)-2(y+3)=0$
$\Rightarrow (y-2)(y+3)=0$
$\Rightarrow (y-2)=0\text{and}(y+3)=0$
$\Rightarrow y=2\text{and}y=-3$
$\Rightarrow 2^x=2\text{and}{2}^x=-3$
Since $2^x$ is an even number so that it can't be equal to $-3$
$\therefore 2^x=2$
$\therefore x=1$
Option D is correct.