Final answer:
To solve the equation e^3x = 12, take the natural logarithm of both sides, isolate x, and then divide by 3. The solution to the equation is approximately ≈ 0.83
Step-by-step explanation:
To solve the equation e^3x = 12, we need to isolate x. To do that, we can take the natural logarithm of both sides of the equation.
The natural logarithm of e^3x is simply 3x.
Therefore, the equation becomes 3x = ln(12). Now, we can divide both sides of the equation by 3 to solve for x.
So x = ln(12)/3.
Using a calculator, we can find that ln(12) ≈ 2.48.
Therefore, the solution to the equation is approximately x ≈ 2.48/3
≈ 0.83 when rounded to the nearest hundredth.