What is the missing exponent in the following equation?

To solve for the missing exponent in the equation:

\[ \frac{e^x}{e^{65}} = e^{38} \]

we can use the properties of exponents. Specifically, we can rewrite the left side:

\[ e^{x - 65} = e^{38} \]

Since the bases are the same (both are base \( e \)), we can set the exponents equal to each other:

\[ x - 65 = 38 \]

Now, solve for \( x \):

\[ x = 38 + 65 \] \[ x = 103 \]

Thus, the missing exponent is:

\[ \boxed{103} \]