To solve this equation, we need to use logarithms.

First, we can simplify the equation by combining like terms:

3^(x+1) + 3^x = 108

Now, we can rewrite the equation using logarithms:

log(3^(x+1) + 3^x) = log(108)

By using the properties of logarithms, we can rewrite the equation as:

log(3^(x)*3) = log(108)

Now, we can simplify the equation further:

(x+1)*log(3) = log(108)

Next, we can isolate x by dividing both sides by log(3):

x+1 = log(108)/log(3)

x = (log(108)/log(3)) - 1

Using a calculator, we can find that x is approximately equal to 3.