Fast and asymptotically efficient one-step and two-steps estimation procedures for the parameters of the location-scale t and log(t) distributions are proposed. They are based on two possible initial guess estimators: the first one is the maximum likelihood estimator on a subsample and the second one is a combination of the empirical median for the location, a slowly converging Hill estimator for the degree of freedom and a maximum likelihood type estimator for the scale. Then, one step or two steps of the Fisher scoring gradient descent method are done in order to correct the initial estimation and reach asymptotical efficiency. The performances of the estimation procedures are evaluated on samples of finite size in terms of mean square error and computation time. An application in economics is also proposed.