We can rewrite 27 as 3^3. So we have:

3^(x+1) = 3^3

By using the rule that states that if two exponential expressions have the same base, then we can equate their exponents, we get:

x + 1 = 3

Solving for x, we get:

x = 2

We can take the logarithm of both sides of the equation using any base, as long as we use the same base for both the logarithm and the exponential expression. Let's use base 3:

log3(3^(x+1)) = log3(27)

By using the rule that states that log(a^b) = b*log(a), we get:

(x+1)log3(3) = log3(27)

Simplifying, we get:

x+1 = 3

Solving for x, we get:

x = 2