I had a similar problem and this scale worked for me like a charm:
breaks = 10**(1:10)
scale_y_log10(breaks = breaks, labels = comma(breaks))
as you want the intermediate levels, too (10^3.5), you need to tweak the formatting:
breaks = 10**(1:10 * 0.5)
m <- ggplot(diamonds, aes(y = price, x = color)) + geom_boxplot()
m + scale_y_log10(breaks = breaks, labels = comma(breaks, digits = 1))
After executing::