Multiplicative operations and invariance of neuronal responses are thought to play important roles in the processing of neural information in many sensory systems. Yet the biophysical mechanisms that underlie both multiplication and invariance of neuronal responses in vivo, either at the single cell or at the network level, remain to a large extent unknown. Recent work on an identified neuron in the locust visual system (the LGMD neuron) that responds well to objects looming on a collision course towards the animal suggests that this cell represents a good model to investigate the biophysical basis of multiplication and invariance at the single neuron level. Experimental and theoretical results are consistent with multiplication being implemented by subtraction of two logarithmic terms followed by exponentiation via active membrane conductances, according to a x 1/b = exp(log(a) - log(b)). Invariance appears to be in part due to non-linear integration of synaptic inputs within the dendritic tree of this neuron.