Simple algebra-calculus question

[lifelearner]

1. Homework Statement , and relevant equations

How is A6 arrived at and *how* did they get the "Q" in A6?

Homework Equations

See above
3. The Attempt at a Solution

Objective: Rid A1 of L. They simply substituted "C" in A2 into A1. But how did they get rid of the L? I don't quite get the algebraic manipulation...please help

 

[lifelearner]

What I specifically do not understand is how the exponents, alpha and beta, have been manipulated to be ratios. The only way I think you can do that is by using logarithms, but I do not quite know how.

Anyone have any ideas?