Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use natural logarithms to solve the equation. Round to the nearest thousandth.
5e2x + 11 = 30
5e^(2x) + 11 = 30
Subtract 11 from both sides:
5e^(2x) = 19
Divide by 5:
e^(2x) = 3.8
Take the natural logarithm of both sides:
ln(e^(2x)) = ln(3.8)
2x = ln(3.8)
Divide by 2:
x = ln(3.8)/2 ≈ 0.867
Therefore, the solution to the equation is x ≈ 0.867.