Solve the equation 3^x = 81.

The solution to the equation 3^x = 81 is x = 4.

To solve this equation, we need to use logarithms. Specifically, we need to take the logarithm of both sides of the equation with respect to the base 3. This gives us:

log3(3^x) = log3(81)

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

x log3(3) = log3(81)

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

x = log3(81)

Now we need to evaluate the logarithm on the right-hand side of the equation. We can use the fact that 81 = 3^4 to rewrite the equation as:

x = log3(3^4)

Using the power rule of logarithms again, we get:

x = 4 log3(3)

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

x = 4

Therefore, the solution to the equation 3^x = 81 is x = 4.