Use the One-to-One Property to solve the equation for x. $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$
A) $x = - 4$
B) $x = 3$
C) $x = 4 , - 1$
D) $x = - 4 , - 1$
E) $x = - 4,1$

Question

Use the One-to-One Property to solve the equation for x.  $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$ 
A) $x = - 4$
B) $x = 3$
C) $x = 4 , - 1$
D) $x = - 4 , - 1$
E) $x = - 4,1$

Quizplus · Accepted Answer

The One-to-One Property of exponential functions states that if $e^a = e^b$, then $a = b$. Applying this to the given equation, we have $x^2 - 4 = 3x$. Rearranging, we get $x^2 - 3x - 4 = 0$, which factors to $(x - 4)(x + 1) = 0$. Thus, $x = 4$ or $x = -1$.

Use the One-To-One Property to Solve the Equation for X ex2−4=e3xe ^ { x ^ { 2 } - 4 } = e ^ { 3 x }ex2−4=e3x

Use the One-To-One Property to Solve the Equation for X $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$