Difference of doing a PSD estimate of data and logarithmic transformed data? What is the difference between doing a PSD estimate with data and the same data but which is logarithmically transformed before the estimate? Does it make the data more sinusoidal in nature?

An exercise in a book asks this question:

"For the lynx data, compare your spectral analysis results from the original data, and the data transformed first by taking the logarithm of each sample and then by subtracting the sample mean of this logarithmic data. Does the logarithmic transformation make the data more sinusoidal in nature?"
The exercise is instructive. Since this is an exercise, I will not do the full problem.  I leave that to you.

grabbing the lynx data from

https://www.encyclopediaofmath.org/index.php/Canadian_lynx_data.

The data is counts and there are no years with a zero count.



and putting it into matlab and taking the log and subtracting the mean of the log,



Would you say that the data looks sine like ?

This technique works on certain kinds of data.  Think of it as a tool and is covered in a number of basic stats book.