Thelogarithmic function restricts a value interval when applied while the exponential one is expanding that interval.

The approximation error is evaluated by thelogarithmic function

Caption: FIGURE 7: Prediction model for the settlement of the road shoulder: (a) hyperbolic function; (b)logarithmic function; (c) power function; (d) exponential function.

Using thelogarithmic function NB model, Xiang Liu [24] and Rong Li (2013) established the frequency forecast model of the highway traffic crash in Ontario, Canada.

It adopts the Schroeder phases as the initial phases and uses variable clipping level based onlogarithmic function in the iteration procedure.

The three data points [C.sup.o] connected with a smooth curve presents alogarithmic function (Figure 6).

Based on the quadratic function and Taylor series, alogarithmic function is constructed and as Lyapunov function, which is applicable to not only Rotary Inverted Pendulum but also the physical systems with the linear or nonlinear models.

Gent and Thomas [16] proposed an empirical model similar to that of Mooney and Rivlin but containing alogarithmic function of the second invariant.