Question

The number of real solutions of the equation ${(2\left|x\right|-1)}^2=\left|x\right|$ which belong to the domain of definition of the function $y=\log (4x-1)$ is

Answer 1

Domain of $y=\log (4x-1)$ is $x>\frac{1}{4}$
${(2\left|x\right|-1)}^2=\left|x\right|\Rightarrow {4\left|x\right|}^2-5\left|x\right|+1=0\Rightarrow (4\left|x\right|-1)(\left|x\right|-1)=0$
$\Rightarrow \left|x\right|=1,\frac{1}{4}\Rightarrow x=\pm 1,\pm \frac{1}{4}$
$\therefore x=1$ is the only valid solution