You can change the colorbar's scale to logarithmic with the following command:
set(gca,'ColorScale','log')
Here is it altogether with random values for y.
x = 1:1000;
y = 100000*rand(1,1000).*rand(1,1000).*rand(1,1000);
scatter(x,y,20,y,'filled')
ah=gca;
ah.YScale = 'log';
colorbar
set(gcf,'color','k')
set(gca,'color','k')
ah.XAxis.Color = 'w';
ah.YAxis.Color = 'w';
fh=gcf;
fh.Children(1).Color = 'w';
colormap(jet)
set(gca,'ColorScale','log')
