  Two general methods for establishing the logarithmic behavior of recursively
defined sequences of real numbers are presented. One is the interlacing method,
and the other one is based on calculus. Both methods are used to prove
logarithmic behavior of some combinatorially relevant sequences, such as
Motzkin and Schr\"oder numbers, sequences of values of some classic orthogonal
polynomials, and many others. The calculus method extends also to two- (or
more-) indexed sequences.
