Give the answer in exact form.
-$$e ^ { 2 x } - 8 e ^ { x } + 15 = 0$$
A) $\left\{ \mathrm { e } ^ { 5 } , \mathrm { e } ^ { 3 } \right\}$
B) $\left\{ \frac { 5 } { e } , \frac { 3 } { e } \right\}$
C) $\{ \ln 5 , \ln 3 \}$
D) $\{ \ln ( - 5 ) , \ln ( - 3 ) \}$

Question

Quizplus · Accepted Answer

This equation is a quadratic in form if we let $u = e^x$, becoming $u^2 - 8u + 15 = 0$. Factoring gives $(u - 5)(u - 3) = 0$, so $u = e^x = 5$ or $u = e^x = 3$. Taking the natural logarithm of both sides gives $x = \ln 5$ or $x = \ln 3$.

Give the Answer in Exact Form e2x−8ex+15=0e ^ { 2 x } - 8 e ^ { x } + 15 = 0e2x−8ex+15=0

Give the Answer in Exact Form $e ^ { 2 x } - 8 e ^ { x } + 15 = 0$