  We consider an inverse problem of recovering the non-linearity in the one
dimensional variable exponent $p(x)$-Laplace equation from the
Dirichlet-to-Neumann map. The variable exponent can be recovered up to the
natural obstruction of rearrangements. The main technique is using a
M\"untz-Sz\'asz theorem after reducing the problem to determining a function
from its $L^p$-norms.
