A growing interest has been witnessed in recent years in multivariate discrete probability models. The multivariate logarithmic series distribution (LSD) is a multivariate analogue of the univariate LSD. This paper investigates the marginal and the conditional distributions of the multivariate LSD. It records its moment properties and also provides some regression and correlation analysis. An interesting modal property of the distribution is discovered. The paper also discusses the estimation of the parameters by the methods of maximum likelihood and unbiased minimum variance. At the end is discussed in detail an application of the multivariate LSD to the field of population and community ecology.