Please enlighten me, what is the logarithm of the numbers on your horizontal axis?
If the answer is the answer I expect, then there is no way to produce a logarithmic axis for negative numbers.
In addition. logarithmic axes are usually used when there are several orders of magnitude (usually several powers of 10) difference between the maximum and minimum values. Fundamentally, I see little value in creating a logarithmic axis for values where there is less than one order of magnitude from max to min.