Find coefficents given equation and three points

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The discussion centers on finding coefficients 'a' and 'b' in the equation log10(y) = a * log10(x) + b using the points (5, 20) and (10, 2). The user, Hkskyy, initially attempted to use simultaneous equations but encountered difficulties with subtraction. Theo advised simplifying the approach by directly substituting the points into the equation to create two linear equations in 'a' and 'b' for easier solving.

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Hkskyy
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Hello,

I hope someone can help me with this. I have an equation:

log10(y) = a * log10(x) + b

or

y = 10^(log10(x)a + b)

I am trying to find a and b given two points. My approach is to use the process of simultaneous equation but I am having problems subtracting the equations.

Points: (5, 20) (10,2)

first equation: 20 = 10^(log10(5)a +b)
second equation: 2 = 10^(log10(5)a +b)

Subtraction: 18 = 10^(log10(5)a +b) - 10^(log10(5)a +b)


My question is if this is a good approach and if I am following the laws. I am trying to fit the equation to the two points.

Thanks all,
 
Last edited:
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Hkskyy - use your first form of the expression with the two points. This will set up two linear equations in a and b that you can solve.
 
Thanks much Theo. I was making it more complicated than it should be.
 

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