  We study a q-logarithm which was introduced by Euler and give some of its
properties. This q-logarithm did not get much attention in the recent
literature. We derive basic properties, some of which were already given by
Euler in a 1751-paper and 1734-letter to Daniel Bernoulli. The corresponding
q-analogue of the dilogarithm is introduced. The relation to the values at 1
and 2 of a q-analogue of the zeta function is given. We briefly describe some
other q-logarithms that have appeared in the recent literature.
