How to do Linearization for Non-linear least squares?

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Linearization in non-linear least squares involves approximating a non-linear function with a linear model around a point. The discussion highlights the use of logarithmic transformation on the dependent variable to facilitate this process. The poster provides a MATLAB example, indicating the need for a method to derive parameters from non-linear data. Additionally, there is a mention of potential issues when the number of x values exceeds y values. Understanding these concepts is crucial for effectively applying non-linear least squares techniques.
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I want to know how to make linearization for some function,...what should by in Non-linear least squares problems.
In my book I have only this example how to do:

http://i.imgur.com/MUFiHkr.pngSomeone could me help how to do, some receipt of method what I need to do?

Non-linear least squares problems was in Matlab:
x = [ 1 2 3 4 5]
y = [ 3.5 2 4 8]

u = log(y)
v = [ones(5,1), x']
btr = x\u'
beta0
...
...
fminsearch
 
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You have more x data values than corresponding y values?
 

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