Solve the equation.
-$$\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }$$
A) $\{ 6,9 \}$
B) $\{ 9 \}$
C) $\{ 6 \}$
D) $\{ - 6 , - 9 \}$

Question

Quizplus · Accepted Answer

The given equation is $\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }$. Simplifying, we get $e^{x^2} \cdot e^{54} = e^{15x}$. Combining the exponents on the left, we have $e^{x^2 + 54} = e^{15x}$. Since the bases are the same, we can set the exponents equal to each other: $x^2 + 54 = 15x$. Rearranging, we get $x^2 - 15x + 54 = 0$, which factors to $(x - 6)(x - 9) = 0$. Thus, $x = 6$ or $x = 9$, making the solution set $\{6, 9\}$.

Solve the Equation (ex)x⋅e54=e15x\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }(ex)x⋅e54=e15x

Solve the Equation $\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }$