that is experimentally measured by adding the molecule to an octanol/water mixture (OW) and by

taking the logarithm of the ratio [[K.sub.(OW)]] of the amount that dissolves in the octanol phase to the amount that dissolves in the water phase.

Formula (1) belongs to a linearized nonlinear time-varying model, replacing variables into multiple linear time-varying models and by

taking the logarithm from formula (1) on both sides it can be transformed into

And for handling nonlinear data fitting problems, the least squares method could only approximate it into a linear problem by

taking the logarithm of both ends which resulted in migration of the optimal solution [9].

Taking the logarithm on both sides of (14), it can be rewritten as

Taking the logarithm of both sides of (1.4) and using Mobius inversion gives (see [BLL98]) the following refinement of (1.2),

Taking the logarithm of both sides of Equation 5, Equation 6 is obtained,

For isothermal conditions,

taking the logarithm of Eq 4 gives:

Taking the logarithm shows that a double logarithmic plot yields straight lines.

By

taking the logarithm in Stirling's Formula, [lim.[n[right arrow][infinity]]] [n.summation over (k=1)] ln k - n(ln n) - 1/2(ln n) + n] = 1/2[ln(2[pi])].

Substituting the last expression into equation (1) and

taking the logarithm of both sides, one obtains:

Taking the logarithm on both sides of (2), it leads to a linear relation between the ln [??] and ln [sigma] for a constant loading temperature:

Taking the logarithm derivative from both sides of (22) we get