Solve the following equation. \( e^{2 x}-7 e^{x}+12=0 \) What is the solution in terms of natural logarithms? Select the corre A. The solution set is \{ \} 3 . The a comma to separate answers as needed. Type an ex B. The solion set is the empty set.

To solve the equation \( e^{2x} - 7e^{x} + 12 = 0 \), we can use substitution. Let \( y = e^{x} \). Then our equation transforms to: \( y^2 - 7y + 12 = 0 \) Factoring this quadratic gives: \( (y - 3)(y - 4) = 0 \) So, \( y = 3 \) or \( y = 4 \). Reverting back to \( x \): 1. From \( y = 3 \): \( e^{x} = 3 \) leads to \( x = \ln(3) \). 2. From \( y = 4 \): \( e^{x} = 4 \) leads to \( x = \ln(4) \). Thus, the solution set is: \(\{ \ln(3), \ln(4) \}\)