Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e2x+ 5 = 27
(1 point)
Responses
1.9924
1.9924
0.9962
0.9962
1.5455
1.5455
0.4327
First, we need to isolate the exponential term:
3e^(2x) + 5 = 27
3e^(2x) = 22
Next, divide both sides by 3:
e^(2x) = 22/3
Now, take the natural logarithm of both sides to solve for x:
ln(e^(2x)) = ln(22/3)
2x = ln(22/3)
x = ln(22/3) / 2
Using a calculator to find ln(22/3) / 2, we get x ≈ 1.992. Therefore, the correct answer is 1.992.