Solve the exponential equation using like bases. (Enter your answers as a comma-separated list.)
\[
\begin{array}{l}
e^{x^{2}+10 x}=\frac{1}{e^{24}} \\
x=\square
\end{array}
\]

Answer

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Answer

Final Answer: \(\boxed{-6, -4}\)

Steps

Step 1 ：The given equation is in the form of \(e^x = e^y\), where x and y are expressions. In such cases, we can equate the expressions x and y. Here, we have \(x^2 + 10x = -24\) (since \(1/e^{24}\) is \(e^{-24}\)). This is a quadratic equation which we can solve for x.

Step 2 ：Solving the quadratic equation \(x^2 + 10x + 24 = 0\), we get the solutions as \(x = -6\) and \(x = -4\).

Step 3 ：These are the values of x for which the given equation holds true.

Step 4 ：Final Answer: \(\boxed{-6, -4}\)

Solve the exponential equation using like bases. (Enter your answers as a comma-separated list.)\[\begin{array}{l}e^{x^{2}+10 x}=\frac{1}{e^{24}} \\x=\square\end{array}\]

Answer

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Solve the exponential equation using like bases. (Enter your answers as a comma-separated list.)
\[
\begin{array}{l}
e^{x^{2}+10 x}=\frac{1}{e^{24}} \\
x=\square
\end{array}
\]