transpose formula when x is power of n

Question

I need help transposing this formula to solve for F0. the problem is that i don't know what to do when Octave is > 2. Apologies if this is a noob question :P

$S_n$ = $\dfrac{F0-2^{Octave} \times 20}{(2^{Octave} \times 20)/12}$

Answer 1

$F_0 = 2^{Oct} \left( 5/3 + 20 \right)$.

Answer 2

And as always.. It was easier than i thought.

My mistake was in the order of operations, using python shell here, so i missed some parentheses. Anyways, the answer is:

$F_0 = S_n \left((2^{Oct} \cdot 20)/12\right) + \left( 2^{Oct} \cdot 20 \right)$.

where $S_n$ is the Music scale and $Oct$ is the octave