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.)

Answer

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Answer

The solution set is $\boxed{3, 6}$.

Steps

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

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

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

Step 4 ：The solution set is $\boxed{3, 6}$.