You cannot take the log of a negative number or 0. The number must be positive and non-zero. This is not Surfer's rule, but a mathematical one. The log of (X) becomes asymptotic as X approaches 0.
If you already have a grid file with Z values that are negative or 0 and you create a contour map and try to set the Level method to Logarithmic, then you will get an error that the minimum contour level must be greater than 0.0. Click OK in the error. You will need to change the Minimum contour value to be >0.0, and then you can change the Level method to Logarithmic.
If you already have a grid file with negative or 0 values for some grid nodes, create an image map (or other map type) and try to change the colormap to use logarithmic scaling, then you will get an error that logarithmic scaling requires positive data. Click OK in the error. You will need to change the Minimum and/or Maximum data value for the colormap so that they are both >0.0.
Updated October 20, 2017