This equation:
$\hspace{1in}X=S\times(P_{FC}/P_{DC})$
Can be rewritten in terms of percentage change over a time period as follows:
$\hspace{1in}x=s+I_{FC}-I_{DC}=s-(I_{DC}-I_{FC})$
How can I actually rewrite this? I think it has something to do with logarithms because the multiplication becomes an addition and the division becomes a subtraction, but I think taking the log on both sides won't give me the answer.
For example,since $x$ is a percentage change over a time period, I figured its this must be true:
$\hspace{1in} x=\frac{X_{2}}{X_{1}}-1$
But $\frac{X_{2}}{X_{1}}-1$ is definitely not equal to $\log X$.
Any hints would be much appreciated. Thank you.