The logarithmic form for turbulent flow analysis guarantees the positivity of the turbulence variables as ${kappa}$ and ${varepsilon}$ of the ${kappa}-{varepsilon}$ model by using the natural logarithm of these variables. In the present study, the logarithmic form is incorporated into the finite element solution procedure for the unsteady turbulent flow analysis. A backward facing step flow using the standard ${kappa}-{varepsilon}$ model and a flow around a 2D square cylinder using the modified ${kappa}-{varepsilon}$ model (the Kato-Launder model) are simulated. These results show that the logarithmic form effectively keeps adequate balance of turbulence variables and makes the analysis stable during transient or unsteady processes.