Composition of series with Mathematica

I am trying to compose two series with Mathematica :

One is f1(x) = ...

The other is x(y) = ...

ComposeSeries quits complaining that the expansion point of the first series
is different from the constant term of the second series
(ComposeSeries::scmp). What I am really trying to do here is to express f
(x) as a series in Log[x] (x is strictly greater than zero), so the second
series is simply the series expansion of Exp[y].

Mathematically, what is the problem with even attempting this operation ?
Can't I replace x by log(z) in the first series, no matter what ?
.