Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$$3 e ^ { x } \left( e ^ { x } - 8 \right) = 5 e ^ { x } - 40$$
A) $\left\{ - \frac { 5 } { 3 } , - 8 \right\}$
B) $\left\{ \ln \left( \frac { 5 } { 3 } \right) , \ln ( 8 ) \right\} ; x \approx 0.5108 , x \approx 2.0794$
C) $\left\{ \frac { 5 } { 3 } , 8 \right\}$
D){ }

Question

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$$3 e ^ { x } \left( e ^ { x } - 8 \right) = 5 e ^ { x } - 40$$
A) $\left\{ - \frac { 5 } { 3 } , - 8 \right\}$
B) $\left\{ \ln \left( \frac { 5 } { 3 } \right) , \ln ( 8 ) \right\} ; x \approx 0.5108 , x \approx 2.0794$
C) $\left\{ \frac { 5 } { 3 } , 8 \right\}$
D){  }

Quizplus · Accepted Answer

First, simplify the equation: $3e^{x}(e^{x} - 8) = 5e^{x} - 40$. Distribute to get $3e^{2x} - 24e^{x} = 5e^{x} - 40$. Rearrange to form a quadratic equation in terms of $e^{x}$: $3e^{2x} - 29e^{x} + 40 = 0$. Factoring or using the quadratic formula gives $e^{x} = \frac{5}{3}$ and $e^{x} = 8$. Taking the natural logarithm of both sides for each solution gives $x = \ln\left(\frac{5}{3}\right)$ and $x = \ln(8)$, with approximate values $x \approx 0.5108$ and $x \approx 2.0794$.

Solve the Equation 3ex(ex−8)=5ex−403 e ^ { x } \left( e ^ { x } - 8 \right) = 5 e ^ { x } - 403ex(ex−8)=5ex−40

Solve the Equation $3 e ^ { x } \left( e ^ { x } - 8 \right) = 5 e ^ { x } - 40$