  We consider one-dimensional Calder\'on's problem for the variable exponent
$p(\cdot)$-Laplace equation and find out that more can be seen than in the
constant exponent case. The problem is to recover an unknown weight
(conductivity) in the weighted $p(\cdot)$-Laplace equation from Dirichlet and
Neumann data of solutions. We give a constructive and local uniqueness proof
for conductivities in $L^\infty$ restricted to the coarsest sigma-algebra that
makes the exponent $p(\cdot)$ measurable.
