Final answer:
To solve the equation 6^(3x) = 36 accurate to three decimal places, we need to use logarithms.
Step-by-step explanation:
To solve the equation 6^(3x) = 36 accurate to three decimal places, we need to use logarithms. Taking the logarithm of both sides of the equation will help us isolate the variable. Applying the logarithmic property, we can rewrite the equation as log6(6^(3x)) = log6(36). Since the logarithm base is 6, we can further simplify this to 3x = log6(36). Next, divide both sides by 3 to solve for x: x = (1/3) * log6(36). Finally, evaluate the expression using a calculator to obtain the numerical approximation for x.