GFR Wrote:b[s]<-n> = b[s]\<n> = s-hexp_b <-n> = s-hlog_b <n> , with back and forward iterations.

Right? ... or ... wrong !!!

Right. We have

f<r>(f<s>(x)) = f<r+s>(x)

f<0>(x) = x

As a derivation:

b [r]\ x = b[r]<-1> x and

x /[r] n = ([r]n)<-1>(x)

Though I think the mind has somewhat to cope with the last line in daily calculation.

And this does also not solve Gottfried's problem of expressing the height h such that b[r]<h> x = y.