Solve the exponential equation below algebraically.
$e ^ { - 6 x } = e ^ { x ^ { 2 } + 5 }$
A) $- 6$ and $- 1$
B) $- 5$ and $- 1$
C) $- 6$ and $- 5$
D) $- 5$ and 6
E) $- 1$ and 6

Question

Quizplus · Accepted Answer

By equating the exponents, we have $-6x = x^2 + 5$. Rearranging gives $x^2 + 6x + 5 = 0$. Solving this quadratic equation gives the roots $-5$ and $-1$.

Solve the Exponential Equation Below Algebraically e−6x=ex2+5e ^ { - 6 x } = e ^ { x ^ { 2 } + 5 }e−6x=ex2+5

Solve the Exponential Equation Below Algebraically $e ^ { - 6 x } = e ^ { x ^ { 2 } + 5 }$