Is it possible to know how many steps are left to reach 1 knowing only x?

The main idea is: when we analyze numbers of the form $n = 3^x + 2^x$ (for $x \ge 1$), we can track the Collatz trajectory using algebra instead of doing it number by number.

Following the rules (if it is odd, multiply by $3$ and add $1$; if it is even, divide by $2$), we see that the exponents move in an orderly way:

1. Start: $3^x + 2^x$ (always odd)
2. Step 1 ($3n+1$): $3^{x+1} + 3 \cdot 2^x + 1$
3. Step 2 (Divide by 2): $\frac{3^{x+1} + 3 \cdot 2^x + 1}{2}$ (dividing the entire sum by 2 yields $\frac{3^{x+1}+1}{2} + 3 \cdot 2^{x-1}$, introducing a fractional term)
4. Next steps: If it turns out odd again, applying the rule once more leads to: $\frac{3^{x+2} + 5}{2} + 9 \cdot 2^{x-1}$

The question

Since this entire process behaves like a predictable algebraic structure that depends solely on the value of $x$, is it possible to create a formula or calculate exactly how many total steps it will take to reach 1 knowing only the number $x$?

In other words, do these expressions allow us to know how many exact ups and downs occur without having to simulate the whole sequence by hand?