  We extend earlier work on leading logarithms in the massive nonlinear O(n)
sigma model to the case of SU(N)xSU(N)/SU(N) which coincides with mesonic
chiral perturbation theory for N flavours of light quarks. We discuss the
leading logarithms for the mass and decay constant to six loops and for the
vacuum expectation value <\bar{q}q> to seven loops. For dynamical quantities
the expressions grow extremely large much faster such that we only quote the
leading logarithms to five loops for the vector and scalar form factor and for
meson-meson scattering. The last quantity we consider is the vector-vector to
meson-meson amplitude where we quote results up to four loops for a subset of
quantities, in particular for the pion polarizabilities. As a side result we
provide an elementary proof that the factors of N appearing at each loop order
are odd or even depending on the order and the remaining traces over external
flavours.
