Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. $$ e^{x+1}=\frac{1}{e} $$ The solution set is $$ \{\square\} $$.

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1. Write the equation:
   $$
   e^{x+1} = \frac{1}{e}
   $$

2. Express the right-hand side as a power of $$ e $$:
   $$
   \frac{1}{e} = e^{-1}
   $$

3. Substitute into the equation:
   $$
   e^{x+1} = e^{-1}
   $$

4. Since the bases are the same, set the exponents equal:
   $$
   x + 1 = -1
   $$

5. Solve for $$ x $$:
   $$
   x = -2
   $$

The solution set is $$ \{-2\} $$.
The solution is $$ x = -2 $$.

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. \[ e^{x+1}=\frac{1}{e} \] The solution set is \( \{\square\} \).

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