Cobb-Douglas functions in economics

[SOLVED] Cobb-Douglas functions in economics

Hi. I'm an economics major. This problem isn't actually required, but I'm trying to learn more about Cobb-Douglas functions.

1. The problem statement, all variables and given/known data
http://rds.yahoo.com/_ylt=A0oGkj3DTedHID4AWKtXNyoA;_ylu=X3oDMTE1OTRmMDcwBHNlYwNzcgRwb3MDMgRjb2xvA3NrMQR2dGlkA01BUDAxMV8xMDI-/SIG=120jm51ch/EXP=1206427459/**http://www.uvm.edu/~wgibson/cobb-douglas.pdf" [pdf] is a description of them. On that first page they go from [tex]U_{0} = X^{B}*Y^{1-B}[/tex]. Then they solve for Y and get [tex]Y = U^{1/1-B}_{0}*X^{-B/1-B}[/tex]. The question is simple: how did they do that algebraically?


2. Relevant equations



3. The attempt at a solution


I tried to sort things around to get their solution. I got [tex]Y^{1-B} = U_{0}/X^{B}[/tex] Assuming that is right, I then took the natural log of both sides and divided both sides by [tex]1-B[/tex]. But here is where I'm stuck. Obviously the -B exponent on X in the solution makes it a fraction, but I'm just too rusty/untalented at this stuff to figure out how dividing by (1-B) can find a way into the exponents of the variables.

Incidentally, how do I group things with fractions in Latex?

Nevermind, I'm retarded. Of course if I take the root (1-B) of both sides I get that answer...duh...still curious about the Latex stuff though...
 
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