wow, here we go again with old out of practice brain.

Question

anonymous · Answer

$$R^{1\beta}=2-\frac{R_{sys}}{R}$$  apparently solves to :

$$\beta=1-\frac{\ln(2-\frac{R_{sys}}{R})}{\ln(R)}$$ (I say apparently)

anonymous · Answer

So there is a conversion rule I am vague on (less that apparently) using ln conversions.  Can anyone give me a hint 1) of the rule here and 2) a web resource of like rules?  Thanks in advanced.

anonymous · Answer

Sorry, starting equation missing '-' so is:

$$R^{1-\beta}=2-\frac{R_{sys}}{R}$$

anonymous · Answer

GAG! DOH!  It clicked.

$$(1-\beta)\ln(R)=\ln(2-\frac{R_{sys}}{R})$$

so:

$$1-\beta=\frac{\ln(2-\frac{R_{sys}}{R})}{\ln(R)}$$

et cetera.

Can I give myself a prize for solving me own problem lol?