Plotting large negative and positive logarithmic scatter plot on both axes

I want to plot two variables which are each a matrix of (500,16) against eachother with each on a logarithmic axis which includes both negative and positive log values. I understand the mathematical 'error' in doing this, but I am comparing changes in each variable (which are positive and negative) and due the small size of the changes, I need to plot them on log axes.
Any help would be appreciated as I have spent a day trying to tweak other matlab answers to be able to do it but have failed.

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Log aside, what do you envision a plot of "two variables which are each a matrix of (500,16) against each other" would be since each so-called "variable" is an array?

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