You want to use a logarithmic axis for a graph.

Use scale_x_log10() and/or scale_y_log10() (Figure 8-26):

library(MASS) # For the data set

# The base plot
p <- ggplot(Animals, aes(x=body, y=brain, label=rownames(Animals))) +
     geom_text(size=3)
p

# With logarithmic x and y scales
p + scale_x_log10() + scale_y_log10()

Figure 8-26. Left: exponentially distributed data with linear-scaled axes; right: with logarithmic axes

With a log axis, a given visual distance represents a constant proportional change; for example, each centimeter on the y-axis might represent a multiplication of the quantity by 10. In contrast, with a linear axis, a given visual distance represents a constant quantity change; each centimeter might represent adding 10 to the quantity.