The rapid growth of the culture of microorganisms in a bioreactor prior to the log phase. After the medium within a bioreactor has been inoculated with a small population of microorganisms, there is an initial lag phase of no growth in which they adjust to their new environment. Cell division then occurs at an increasing rate until the maximum growth rate is reached. The log or exponential phase corresponds to the rapid cell division such that the logarithm of the population increase with time is constant. As the substrate eventually becomes exhausted, this is then followed by a deceleration phase prior to the stationary phase.