Solve the equation.
$e^{x^{2}} = e^{9 x} \cdot \frac{1}{e^{18}}$

The solution set is ${◻$ .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Answer

Expert–verified

Hide Steps

Answer

The solution set is $3, 6$ .

Steps

Step 1 ：Simplify the equation by using the properties of exponents.

Step 2 ：Set the exponents equal to each other: $x^{2} = 9 x - 18$ .

Step 3 ：Solve for $x$ : $x = 3, x = 6$ .

Step 4 ：The solution set is $3, 6$ .