Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e^2x + 5 =27
3e^(2x) + 5 = 27
3e^(2x) = 22
e^(2x) = 22/3
2x = ln(22/3)
2x ≈ ln(7.333)
x ≈ ln(7.333)/2
x ≈ 0.847
Therefore, the solution to the equation is x ≈ 0.847.