Questions: Solve the equation. ln e^x = 8 The solution set is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

$Solve the equation. ln e^x = 8 The solution set is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)$

Transcript text: Solve the equation. $\ln e^{x}=8$ The solution set is $\square$ \}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Solution

Solution Steps

To solve the equation $\ln e^{x} = 8$, we can use the property of logarithms that states $\ln e^{x} = x$. Therefore, the equation simplifies to $x = 8$.

Step 1: Simplify the Equation

We start with the equation: \[ \ln e^{x} = 8 \] Using the property of logarithms, we know that: \[ \ln e^{x} = x \] Thus, we can rewrite the equation as: \[ x = 8 \]

Step 2: State the Solution Set

The solution set for the equation is: \[ \{ 8 \} \]