Solve the equation. Give the answer in exact form.
-$$e ^ { 2 x } - 8 e ^ { x } + 12 = 0$$
A) $\left\{ \mathrm { e } ^ { 2 } , \mathrm { e } ^ { 6 } \right\}$
B) $\{ \ln 2 , \ln 6 \}$
C) $\left\{ \frac { 2 } { \mathrm { e } } , \frac { 6 } { \mathrm { e } } \right\}$
D) $\{ \ln ( - 2 ) , \ln ( - 6 ) \}$

Question

Quizplus · Accepted Answer

This equation is a quadratic in form if we let $u = e^x$, becoming $u^2 - 8u + 12 = 0$. Solving this quadratic equation gives $u = 2$ and $u = 6$. Reverting back to the original variable, we have $e^x = 2$ and $e^x = 6$, which leads to $x = \ln 2$ and $x = \ln 6$.

Solve the Equation e2x−8ex+12=0e ^ { 2 x } - 8 e ^ { x } + 12 = 0e2x−8ex+12=0

Solve the Equation $e ^ { 2 x } - 8 e ^ { x } + 12 = 0$