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 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 the logarithmic function
NB model, Xiang Liu  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
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  proposed an empirical model similar to that of Mooney and Rivlin but containing a logarithmic function
of the second invariant.