Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e^2x + 5 =27
A) 1.9924
B) 0.9962
C) 1.5455
D) 0.4327
Starting with the equation 3e^(2x) + 5 = 27, we first subtract 5 from both sides to isolate the exponential term:
3e^(2x) = 22
Next, divide by 3:
e^(2x) = 22/3
Take the natural logarithm of both sides:
ln(e^(2x)) = ln(22/3)
2x = ln(22/3)
Divide by 2 to solve for x:
x = ln(22/3) / 2 ≈ 1.5455
Therefore, the correct answer is:
C) 1.5455