Question

Sum of all real values of $x$ satisfying the equation ${\log }_p({\log }_4|x|-2+p^x)=x,p>2$ is

• A. $32$
• B. $16$
• C. $8$
• D. $0$

Answer 1

The correct option is D $0$

${\log }_4\left|x\right|-2+p^x=p^x$

$\Rightarrow {\log }_4\left|x\right|-2=0$

$\Rightarrow {\log }_4\left|x\right|=2$

$\Rightarrow \left|x\right|=4^2=16$

$\Rightarrow x=+16$ and $-16$

$\therefore$ Sum of all real values $=16+(-16)=0$