Problem
Solve the equation. \[ e^{x^{2}}=e^{9 x} \cdot \frac{1}{e^{18}} \] The solution set is $\{\square$. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Solution
Step 1 ：Simplify the equation by using the properties of exponents.
Step 2 ：Set the exponents equal to each other: \(x^{2} = 9x - 18\).
Step 3 ：Solve for \(x\): \(x = 3, x = 6\).
Step 4 ：The solution set is \(\boxed{3, 6}\).
