## given u=-28.593*ln(k)+144.76, empirically define c, j

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mdr
Posts: 1
Joined: Tue Sep 14, 2010 1:45 am
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### given u=-28.593*ln(k)+144.76, empirically define c, j

I have some given data, which result in a logrithmic trendline of
u = -28.593*ln(k) + 144.76

The object is to empirically define "c" and "j" in the following equation by back substitution:
u = c*ln(j/k) ; only valid where k approaches j

My thought is to set the equations equal to each other, but then I get stuck:
-28.593*ln(k) + 144.76 = c*ln(j/k)

Any ideas?

odysseus
Posts: 10
Joined: Sat Jul 25, 2009 3:07 pm

### Re: given u=-28.593*ln(k)+144.76, empirically define c, j

u = -28.593*ln(k) + 144.76

The object is to empirically define "c" and "j" in the following equation by back substitution:
u = c*ln(j/k) ; only valid where k approaches j
You can use log rules to take the multiplier out front of the logarithmic term inside as an exponent. Then you can convert 144.76 to a logarithm by using ln(x)=144.76, so x=e^144.76. Once you have the right side converted into the sum of two log terms, you can combine then into one log term. Does that do what you need?