Solve the equation.
-$$e ^ { 3 x - 1 } = \left( e ^ { 2 } \right) ^ { - x }$$
A) $\{ 1 \}$
B) $\{ 0 \}$
C) $\left\{ \frac { 1 } { 5 } \right\}$
D) $\left\{ \frac { 3 } { 4 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $e^{3x-1} = (e^2)^{-x}$, we first simplify the right side to $e^{-2x}$ because $(e^2)^{-x} = e^{2(-x)} = e^{-2x}$. Then, we set the exponents equal to each other since the bases are the same: $3x - 1 = -2x$. Solving for $x$, we get $5x = 1$, which simplifies to $x = \frac{1}{5}$.

Solve the Equation e3x−1=(e2)−xe ^ { 3 x - 1 } = \left( e ^ { 2 } \right) ^ { - x }e3x−1=(e2)−x

Solve the Equation $e ^ { 3 x - 1 } = \left( e ^ { 2 } \right) ^ { - x }$