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Find a logarithmic equation that relates y and x

X:1, 2 , 3, 4, 5, 6
Y:0.5, 2.8282, 7.968, 18, 22, 23.8

I took that natural log (ln) of each of these numbers and came up with this-

ln(x): 0, 0.693, 1.099, 1.386, 1.609, 1.792
ln(y): -0.693, 1.040. 2.075, 2.890, 3.090, 3.170

I don't think these points have a linear slope like the rest of the problems I have done like this do so i am unsure how to find that logarithmic equation.



Answer :

Logarithms are only able to make an equation linear if it is an exponential function.  For example, [tex]y= e^{x} [/tex] can be made linear by taking the natural logarithm of each side, causing it to become [tex]ln(y)=ln( e^{x})[/tex]. After some simplifying, you are left with [tex]ln(y)=x[/tex]. You are then able to plot ln(y) vs. x to get a linear fit. 

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