Answer:
Let's denote e^x as u.
The equation can be written as u^2 - u - 2 = 0.
Factoring the quadratic equation, we have (u - 2)(u + 1) = 0.
Setting each factor equal to zero, we obtain u - 2 = 0 and u + 1 = 0.
Solving the equations, we find u = 2 and u = -1.
Since e^x cannot be negative, we discard u = -1.
Hence, e^x = 2.
Taking the natural logarithm of both sides, we have x = ln(2).
Round to the nearest hundredth, x = 0.69. Answer: \boxed{0.69}.
Explanation: