Use natural logarithms to solve the equation.

Question

e^3x =14

Round to two decimal places.

Answer 1

To solve the equation e^3x = 14 using natural logarithms, we take the natural logarithm of both sides:

ln(e^3x) = ln(14)
3x = ln(14)

Now we solve for x:

x = ln(14)/3
x ≈ ln(14)/3 ≈ 0.94

Therefore, the solution to the equation e^3x = 14 is x ≈ 0.94.