The

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

The approximation error is evaluated by the

logarithmic functionCaption: FIGURE 7: Prediction model for the settlement of the road shoulder: (a) hyperbolic function; (b)

logarithmic function; (c) power function; (d) exponential function.

Using the

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

The forecast was done by analyzing Instagram's user growth patterns using a

logarithmic function for the projection.

It adopts the Schroeder phases as the initial phases and uses variable clipping level based on

logarithmic function in the iteration procedure.

The three data points [C.sup.o] connected with a smooth curve presents a

logarithmic function (Figure 6).

The exponential function, linear function,

logarithmic function, quadratic polynomial, and power functions were used to match the data, and the matching GFI (goodness of fit index) obtained from various functions are collected.

Based on the quadratic function and Taylor series, a

logarithmic 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.

One day I stumbled across the Burr-Brown data book, an analog treasure chest brimming with multipliers, dividers, RMS-to-DC converters, and the LOG 100 amplifier, which generated a voltage output that was a

logarithmic function of the input current.

Gent and Thomas [16] proposed an empirical model similar to that of Mooney and Rivlin but containing a

logarithmic function of the second invariant.