To solve for \( x \) in the ratio \( 12:36 \) such that it is equivalent to \( x:3 \), we start by setting up the equation based on the property of equivalent ratios:
\[ \frac{12}{36} = \frac{x}{3} \]
Next, we simplify the left side:
\[ \frac{12}{36} = \frac{1}{3} \]
Thus, we have:
\[ \frac{1}{3} = \frac{x}{3} \]
Next, we can cross-multiply:
\[ 1 \cdot 3 = x \cdot 3 \] \[ 3 = x \]
Therefore, the equivalent ratio is:
\[ x:3 \quad \text{where } x = 1. \]
So, the final answer is \( \boxed{1} \).