Using Graph to determine constants in equation

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To determine the constants k and n in the equation F = x + kx^n, the correct approach involves using logarithmic transformations. The initial assumption that log(F) can be expressed as the sum of logs is incorrect; instead, log(F - x) should be used. By plotting log(F - x) against log(x), a straight line will emerge, where the y-intercept represents log(k) and the slope corresponds to n. This method allows for accurate calculation of both constants k and n. The discussion emphasizes the importance of proper logarithmic manipulation in mathematical modeling.
yardy_genius
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Hello,

i have the equation F= x + kx^n

I am trying to determine the constants k and n? where i have the ranges for F and x

is what i am doing correct?

log F= logx + logk+ nlogx

log F= logx(1+n) + logk


ok i would then plot logF vs Log x. if i am correct logk = y intercept and from that k can be calculated. How would i use the gradient to find the value of n. can someone please give me some assistance. much appreciated.
 
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yardy_genius said:
Hello,

i have the equation F= x + kx^n

I am trying to determine the constants k and n? where i have the ranges for F and x

is what i am doing correct?

log F= logx + logk+ nlogx
No, it is WRONG... log(a+b) is not equal to log(a )+ log(b)

But log(F-x)=log(kx^n)= logk+n logx.

Plot out log(F-x) in terms of logx. It has to be a straight line, with y-intercept logk and slope n.

ehild
 
Last edited:
ehild said:
No, it is WRONG... log(a+b) is not equal to log(a )+ log(b)

But log(F-x)=log(kx^n)= logk+n logx.

Plot out log(F-x) in terms of logx. It has to be a straight line, with y-intercept logk and slope n.

ehild

thank you very much for that correction!
 
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