We want to find the value of $X$ in the given situation.
We are given that $f(2) = f^a(2)$, where $f^a(2)$ means the function $f(x)$ is nested $a$ times.
To find the smallest value of $a$ that satisfies this equation, we can start by evaluating $f(2)$ and $f^a(2)$.
According to the definition of the function $f(x)$, we have:
$f(2) = 2 + 3 = 5$
Now, let's evaluate $f^a(2)$ by nesting the function $f(x)$ $a$ times:
$f^a(2) = f(f^{a-1}(2))$
$f^a(2) = f(f(f^{a-2}(2)))$
...
$f^a(2) = f(f(f(f(f(f(f(2)))))))$
To simplify this expression, we can substitute the values from the definition of the function $f(x)$ at each step:
$f^a(2) = f(f(f(f(f(f(f(2)))))))$
$f^a(2) = f(f(f(f(f(f(7(2)))))))$
$f^a(2) = f(f(f(f(f(7(7(2)))))))$
$f^a(2) = f(f(f(f(7(7(7(2)))))))$
$f^a(2) = f(f(f(7(7(7(7(2)))))))$
$f^a(2) = f(f(7(7(7(7(7(2)))))))$
$f^a(2) = f(7(7(7(7(7(7(2)))))))$
$f^a(2) = 7(7(7(7(7(7(7(2)))))))$
$f^a(2) = 7^7(2)$
Now, we can set up the equation $f(2) = f^a(2)$ and solve for $a$:
$5 = 7^7(2)$
Dividing both sides of the equation by 2, we get:
$2.5 = 7^7$
To find the value of $X$, we need to find the smallest integer value of $X$ that satisfies this equation.
By testing different values of $X$, we find that $X = 3$ is the smallest integer value that satisfies the equation $2.5 = 7^7$.
Therefore, the value of $X$ is 3.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Let \[f(x) = \left\{
\begin{array}{cl}
\frac{x}{21} & \text{ if }x\text{ is a multiple of X and 7}, \\
3x & \text{ if }x\text{ is only a multiple of 7}, \\
7x & \text{ if }x\text{ is only a multiple of 3}, \\
x+3 & \text{ if }x\text{ is not a multiple of 3 or 7}.
\end{array}
\right.\]If $f^a(x)$ means the function is nested $a$ times (for example, $f^2(x)=f(f(x))$), what is the smallest value of $a$ greater than 1 that satisfies $f(2)=f^a(2)$?
If we know the answer to the above question is 7, what is the value of unknown variable X?

### Answer:
