Which is the solution of the equation e^{3x}=4 ? x=ln(4/3) x=4/3e x=In4/3 x=squared(In4/2)

Step 1 ：The equation is in the form of \(e^{3x}=4\). To solve for x, we need to take the natural logarithm (ln) of both sides. This will allow us to isolate x on one side of the equation.

Step 2 ：Taking the natural logarithm of both sides, we get \(3x = ln(4)\).

Step 3 ：To isolate x, we divide both sides by 3, giving us \(x = \frac{ln(4)}{3}\).

Step 4 ：Using a calculator or Python, we find that \(x = 0.46209812037329684\).

Step 5 ：Final Answer: The solution to the equation \(e^{3x}=4\) is \(\boxed{0.46209812037329684}\).