How to Perform Logarithmic Regression by Hand?

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To perform logarithmic regression by hand, the model can be expressed as y = b1 + b2ln(x). This can be approached using the least squares method by transforming the variable x into x' = ln(x). By conducting a linear regression of y against x', the coefficients b1 and b2 can be determined. This method allows for the application of linear regression techniques to logarithmic data. Understanding this transformation is key to performing logarithmic regression manually.
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I'm trying to write some code to do a regression on data weight (x) and time (y). As best as I can tell, the model should be y = b1 + b2ln(x), but I don't know how you can do this by hand (I know how to in R...). I also know how to do a simple linear regression by hand.

Can it be done using the least squares method?
 
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Well, this is a linear equation in x'=ln(x). So you could do a linear regression of y vs x'.
 

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