The logarithms of negative numbers and zero are simply not defined

Let’s start with the fundamental definition of a logarithm. If 10L = Z, then L is the logarithm (base 10) of Z. If L is a negative value, then Z is a positive fraction less than 1.0. If L is zero, then Z equals 1.0. If L is greater than 0, then Z is greater than 1.0. Note that there no value of L will result in a value of Z that is zero or negative. Logarithms are simply not defined for zero or negative numbers.

Bottom line: A logarithmic axis can only plot positive values. There simply is no way to put negative values or zero on a logarithmic axis.

A trick to plot zero on a logarithmic axis in Prism

If you really want to include zero on a logarithmic axis, you’ll need to be clever. Don’t enter 0, instead enter as a small number. For example, if the smallest value in your data is 0.01, enter the zero value as 0.001. Then use the Format Axis dialog to create a discontinuous axis, and use the Additional ticks feature of Prism to label that spot on the axis as 0.0.