f(x)= a+b*lnx - Math Central

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Question from Kevin, a student:

How do I find the curve, algebraically on paper, for f(x)= a+b*lnx with data points
(6,1303) (9,1639). I can do it with LnReg on a calculator but I want to know how
to get the same results or close to the same results by working it out on paper.
When I run it through the LnReg on the calculator I get, f(x)=181.792+828.678 Ln x.
How did it achieve this solution?

Hi Kevin,

I would substitute the two data points into the equation. For the first point that is

\[f(6) = a + b \times \ln(6) = a + 1.7918 \; b = 1303.\]

Do the same for the second point and then you will have two linear equations for $a$ and $b$ which you can solve.

Penny

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