In the case combine(f, ln), expressions involving sums of logarithms are combined by applying the following transformations:

where the coefficient $a$ must be a rational constant and the argument of $x$ and $y$ must be in the region where this transformation is valid, unless 'symbolic' is specified.

In the case combine(f, ln, t), the first transformation is done if the coefficient $a$ is of type t, and the third if the coefficient -1 is of type t. Often it is useful to restrict the transformation to be done only if $a$ is an integer instead of a rational. Also, by specifying the type anything, the transformation is done in all valid cases, provided of course that the coefficient $a$ itself is not a logarithm.

$\mathrm{combine}\left(3\ln \left(2\right)-2\ln \left(3\right)\,\ln \right)$

$6\ln \left(\frac{\sqrt{2}{3}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{3}\right)$

$\mathrm{combine}\left(a\ln \left(x\right)+3\ln \left(x\right)-\ln \left(1-x\right)+\frac{\ln \left(1+x\right)}{2}\,\ln \right)$

$a\ln \left(x\right)+3\ln \left(x\right)+\ln \left(\sqrt{1+x}\right)-\ln \left(1-x\right)$

$\mathrm{assume}\left(a\&comma;\mathrm{real}\right)\&semi;$$\mathrm{assume}\left(0<x\right)$

$\mathrm{combine}\left(a\ln \left(x\right)+3\ln \left(x\right)-\ln \left(1-x\right)+\frac{\ln \left(1+x\right)}{2}\&comma;\ln \right)$

$\mathrm{a~}\ln \left(\mathrm{x~}\right)-\ln \left(\frac{1-\mathrm{x~}}{{\mathrm{x~}}^3\sqrt{1+\mathrm{x~}}}\right)$

$\mathrm{combine}\left(a\ln \left(x\right)+3\ln \left(x\right)-\ln \left(1-x\right)+\frac{\ln \left(1+x\right)}{2}\&comma;\ln \&comma;\mathrm{integer}\right)$

$\mathrm{a~}\ln \left(\mathrm{x~}\right)+\frac{\ln \left(1+\mathrm{x~}\right)}{2}-\ln \left(\frac{1-\mathrm{x~}}{{\mathrm{x~}}^3}\right)$

$\mathrm{combine}\left(a\ln \left(x\right)+3\ln \left(x\right)-\ln \left(1-x\right)+\frac{\ln \left(1+x\right)}{2}\&comma;\ln \&comma;\mathrm{anything}\right)$

$-\ln \left(\frac{1-\mathrm{x~}}{{\mathrm{x~}}^{\mathrm{a~}}{\mathrm{x~}}^3\sqrt{1+\mathrm{x~}}}\right)$

$\mathrm{additionally}\left(x\&comma;\mathrm{RealRange}\left(0\&comma;1\right)\right)$

$\mathrm{combine}\left(a\ln \left(x\right)+3\ln \left(x\right)-\ln \left(1-x\right)+\frac{\ln \left(1+x\right)}{2}\&comma;\ln \&comma;\mathrm{anything}\right)$

$\ln \left(\frac{{\mathrm{x~}}^{\mathrm{a~}}{\mathrm{x~}}^3\sqrt{1+\mathrm{x~}}}{1-\mathrm{x~}}\right)$

$\mathrm{combine}\left(b\ln \left(y\right)+3\ln \left(y\right)-\ln \left(1-y\right)+\frac{\ln \left(1+y\right)}{2}\&comma;\ln \&comma;\mathrm{anything}\&comma;\mathrm{symbolic}\right)$

$\ln \left(\frac{y^b{y}^3\sqrt{1+y}}{1-y}\right)$