What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.

The equation is:

[e^x] [e^ (2x) ] = 4

1) Applying property of multiplication of powers wiith same base = >

e ^ (x + 2x) = 4

=> e ^ (3x) = 4

2) Applying logarigth properties

3x = ln (4)

=> x = ln (4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

Answer: x = ln (4) / 3 ≈ 0.4621