We need to solve the equation $3 \cdot 3^{x+1} = 27$ for $x$.

1. Problem Description

We need to solve the equation $3 \cdot 3^{x+1} = 27$ for $x$.

2. Solution Steps

First, we can rewrite the left side of the equation using the rule $a^m \cdot a^n = a^{m+n}$. In our case, we have $3^1 \cdot 3^{x+1} = 3^{1 + (x+1)} = 3^{x+2}$. So the equation becomes:

$3^{x+2} = 27$

Now, we can express 27 as a power of 3: $27 = 3^3$.

So the equation is:

$3^{x+2} = 3^3$

Since the bases are equal, we can equate the exponents:

$x+2 = 3$

Now, solve for $x$ by subtracting 2 from both sides:

$x = 3 - 2$

$x = 1$

3. Final Answer

$x = 1$