Final answer:
To solve the equation 3 ln(3x) = 9 for x, divide both sides by 3, exponentiate to remove the natural logarithm, and then divide by 3 again to find x ≈ 6.69 when rounded to the nearest hundredth.
Step-by-step explanation:
To solve for x in the equation 3 ln(3x) = 9, you should first divide both sides of the equation by 3 to simplify it. This gives you ln(3x) = 3. To get rid of the natural logarithm, use the property that if ln(y) = z, then y = e^z. Apply this to ln(3x) = 3 to get 3x = e^3. Now divide both sides by 3 to solve for x, resulting in x = e^3 / 3. Finally, use a calculator to find the value of e^3, which is about 20.0855, and divide it by 3 to get the value of x, rounding to the nearest hundredth if necessary.
x ≈ 20.0855 / 3 ≈ 6.69 (rounded to two decimal places)