Question 246244: I am deriving the Hill equation:
V(s)=Vmax(s^n/(Km^n+s^n))
to show that nlns=nlnKm+ln(V/(Vmax-V) (a linear form)
I was told that this involved simple algebra.
If i divide both sides by Vmax:
V/Vmax=s^n/(Km^n+s^n)
then take the logarithm on both sides:
this is where my algebra skills are rusty.
use the quotient rule? and this is where i'm having difficulty...
logV-logVmax= nlogs-log(Km^n+s^n)
logV-logVmax= nlogs-nlogKm-nlogs,which is clearly wrong.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! You are correct down to the last step, but your last step is wrong!! There is NO DISTRIBUTIVE property in LOGARITHMS! In other words, log(x+y) does NOT equal log(x) + log(y).
You are correct to here:
logV-logVmax= nlogs-log(Km^n+s^n)
Now, solve for nlogs by addding +log(Km^n+s^n} to each side:
log V + log(Km^n+s^n) - logVmax= nlogs
Then apparently, you have to solve for Km^n+s^n in the original equation, Km^n+s^n = Vmax*s^n/V(s).
I'm not sure how to finish this, but here is a thought for you.
and substitute this into the equation above:
log V + log(Km^n+s^n) - logVmax= nlogs
log V + log(Vmax*s^n/V(s)) - logVmax= nlogs
Good luck. If I get time, I'll come back and give this some more thought. Meantime, maybe you can re-post this or work on it yourself.
Dr. Robert J. Rapalje
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