Solve the equation 3^x = 27.

The solution to the equation 3^x = 27 is x = 3.

To solve this equation, we need to use logarithms. Taking the logarithm of both sides of the equation with base 3, we get:

log3(3^x) = log3(27)

Using the power rule of logarithms, we can simplify the left-hand side of the equation:

x log3(3) = log3(27)

Since log3(3) = 1, we can simplify further:

x = log3(27)

Using the change of base formula, we can express log3(27) in terms of a more familiar logarithm:

x = log3(27) = log(27) / log(3)

Using a calculator, we can evaluate log(27) and log(3):

x = 3

Therefore, the solution to the equation 3^x = 27 is x = 3.