Logarithmic color scale not in base 10

I have 3 numpy arrays I'm trying to plot in a scatter plot, where the data is visualised on a color scale. This is the line I use for the plot.

plt.scatter(y1, x1, c = jm, s = 3, cmap = 'jet', marker = '.', linewidths = 0, norm = colors.LogNorm())

How do I plot this on a logarithmic color scale with a base other than 10?