Question

What is the missing exponent in the following equation?
e?/e to the power of 65 = e to the power of 38
(1 point)

Answer 1

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:

\[
\boxed{103}
\]