You can log your y-values for the plot and add a custom log y-axis afterwards.
Here is an example for a table object of random normal distribution numbers:
# data
count = table(round(rnorm(10000)*2))
# plot
plot(log(count) ,type="h", yaxt="n", xlab="position", ylab="log(count)")
# axis labels
yAxis = c(0,1,10,100,1000)
# draw axis labels
axis(2, at=log(yAxis),labels=yAxis, las=2)