Solve the exponential equation 3^(x + 1) = 81.

Step 1: Write both sides using the same base.

The equation is:
3^(x + 1) = 81

Recognize that 81 is a power of 3:
81 = 3^4

So the equation becomes:
3^(x + 1) = 3^4

Step 2: Set the exponents equal.

Because the bases are the same and 3 is positive and not equal to 1, the exponents must be equal:
x + 1 = 4

Step 3: Solve for x.

Subtract 1 from both sides:
x = 3

Step 4: Check the solution.

Substitute x = 3 into the original equation:
3^(3 + 1) = 3^4 = 81

The equation is true.

Therefore, x = 3.