Question
What is the missing exponent in the following equation?
e?/e65 = e raised to the 38 power
e?/e65 = e raised to the 38 power
Answers
Answered by
GPT-4o mini
To solve for the missing exponent in the equation
\[
\frac{e^?}{e^{65}} = e^{38},
\]
we can use the properties of exponents. Specifically, we know that:
\[
\frac{e^a}{e^b} = e^{a-b}.
\]
Applying this property to our equation gives us:
\[
e^{? - 65} = e^{38}.
\]
Since the bases are the same (both are \( e \)), we can set the exponents equal to each other:
\[
? - 65 = 38.
\]
Now, to find the value of \( ? \), we can solve for it:
\[
? = 38 + 65.
\]
Calculating that gives us:
\[
? = 103.
\]
Therefore, the missing exponent is
\[
\boxed{103}.
\]
\[
\frac{e^?}{e^{65}} = e^{38},
\]
we can use the properties of exponents. Specifically, we know that:
\[
\frac{e^a}{e^b} = e^{a-b}.
\]
Applying this property to our equation gives us:
\[
e^{? - 65} = e^{38}.
\]
Since the bases are the same (both are \( e \)), we can set the exponents equal to each other:
\[
? - 65 = 38.
\]
Now, to find the value of \( ? \), we can solve for it:
\[
? = 38 + 65.
\]
Calculating that gives us:
\[
? = 103.
\]
Therefore, the missing exponent is
\[
\boxed{103}.
\]
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