  We find solution to the metric function f(r)=0 of charged BTZ black hole
making use of the Lambert function. The condition of extremal charged BTZ black
hole is determined by a non-linear relation of M_e(Q)=Q^2(1-\ln Q^2). Then, we
study the entropy of extremal charged BTZ black hole using the entropy function
approach. It is shown that this formalism works with a proper normalization of
charge Q for charged BTZ black hole because AdS_2 x S^1 represents near-horizon
geometry of the extremal charged BTZ black hole. Finally, we introduce the
Wald's Noether formalism to reproduce the entropy of the extremal charged BTZ
black hole without normalization when using the dilaton gravity approach.
