Hi:
Mathematically, what's the value of log(-1)? So it's impossible to use the real logarithm axis.
So I supposed your data is in a really wide range and you want to plot them tight. An workaround as below:

Column A and B are raw data, and the other columns are:
Col(C) = -log(-Col(A));
Col(D) = Col(B);
And Column E is just the same data from Column A, but sort ascendingly. Then we will use this column E as axis ticks. Plot column C & D, and double-click the X axis to bring up X Axis property dialog. On Tick Labels tab, use Tick-indexed dataset Type and assign column E to Dataset drop down:

Then you will get something like:

Note that it's not really log scale. The scale still linear, but we use different tick labels.
Hope it helps.
Thanks
Larry
OriginLab Technical Services