To solve the equation \( \frac{27}{3^x} = 3 \), follow these steps:

1. **Rewrite 27 as a power of 3:**
\[
27 = 3^3
\]
So the equation becomes:
\[
\frac{3^3}{3^x} = 3
\]

2. **Simplify the left side using the properties of exponents:**
\[
\frac{3^3}{3^x} = 3^{3-x}
\]
So the equation now is:
\[
3^{3-x} = 3^1
\]

3. **Since the bases are the same, set the exponents equal to each other:**
\[
3 - x = 1
\]

4. **Solve for \( x \):**
\[
3 - x = 1
\]
Subtract 3 from both sides:
\[
-x = 1 - 3
\]
\[
-x = -2
\]
Multiply both sides by -1:
\[
x = 2
\]

So, the solution is \( x = 2 \).