Given the equation $3^x + 3^{x+1} = 108$. We can rewrite $3^{x+1}$ as $3^x \cdot 3^1$. So, the equation becomes $3^x + 3^x \cdot 3 = 108$. Factor out $3^x$: $3^x(1 + 3) = 108$. This simplifies to $3^x(4) = 108$. Divide by $4$: $3^x = \frac{108}{4} = 27$. Since $27 = 3^3$, we have $3^x = 3^3$. Therefore, $x = 3$.