I want to format my x-axis in log2(n+1) format so the x-axis labels correspond to 1, 2, 4, 16 and so on.
Input:
x <- c(1, 2, 3, 11, 15)
y <- c(1.1, 1.2, .4, 2.1, 1.5)
plot(log2(x + 1), y, axes=FALSE)
axis(1, at=(labels=as.character(formatC(x))), cex.axis=0.9)
But plot I get still has the original x-axis values.

How can I make my x-axis powers of 2 (1, 2, 4, 16, etc.)?
I guess this is what you want.
It might also be useful to calculate equally spaced labels: