Q. The product of all solutions of the equation $e^{5(\log_e x)^2+3}=x^8$, $x>0$, is :
A) $e^{8/5}$
B) $e^{6/5}$
C) $e^2$
D) $e$
Explanation
[Solution by Dr. Abubacker] Let $t=\ln x$: $5t^2+3=8t\Rightarrow t=1,\frac35$. The product of the solutions is $e^{t_1+t_2}=e^{8/5}$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.