jee-main 2025 Q4

jee-main · India · session1_22jan_shift1 Exponential Equations & Modelling Solve Exponential Equation for Unknown Variable
The product of all solutions of the equation $\mathrm { e } ^ { 5 \left( \log _ { \mathrm { e } } x \right) ^ { 2 } + 3 } = x ^ { 8 } , x > 0$, is:
(1) $e ^ { 8 / 5 }$
(2) $e ^ { 6 / 5 }$
(3) $e ^ { 2 }$
(4) e
The product of all solutions of the equation $\mathrm { e } ^ { 5 \left( \log _ { \mathrm { e } } x \right) ^ { 2 } + 3 } = x ^ { 8 } , x > 0$, is:\\
(1) $e ^ { 8 / 5 }$\\
(2) $e ^ { 6 / 5 }$\\
(3) $e ^ { 2 }$\\
(4) e