Here a simple solution with Plots.jl, really simple:
using Plots; gr(dpi=600)
x = 1:1000; y = log.(x)
f(x) = 1/x
p1 = plot(x, y, c=:blue, xlabel="x", ylabel="y")
xt = xticks(p1)[1][1]
str2 = string.(round.(f.(xt), digits=5))
plot!(twiny(), x, y, c=:blue, xticks=(xt, str2), xlabel="f(x) scale")
