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SolveTools

 Combine
 perform various combining of the expressions

 Calling Sequence Combine(expr, options)

Parameters

 expr - expression options - (optional) one or more of 'ln', 'exp', or 'power'

Description

 • The Combine command combines expressions.
 • The Combine command performs the following transformations after calling SolveTools[CancelInverses] on the expr first.
 • If the option 'ln' is specified, the transformation is the following.

$aj\mathrm{ln}\left(x\right)+\dots +ai\mathrm{ln}\left(y\right)\to a\mathrm{ln}\left({x}^{j}{y}^{i}\right)+\dots$

 • If the option 'exp' is specified, the transformations are the following.

$\mathrm{exp}{\left(x\right)}^{i}\dots \mathrm{exp}{\left(y\right)}^{j}\to \mathrm{exp}\left(ix+jy\right)\dots$

$\mathrm{exp}{\left(x\right)}^{b}\to \mathrm{exp}\left(xb\right)$

 • If the option 'power' is specified, the transformations are the following.

${\left({x}^{b}\right)}^{i}\dots {\left({x}^{c}\right)}^{j}\to {x}^{ib+jc}\dots$

${\left({x}^{y}\right)}^{z}\to {x}^{yz}$

${a}^{b}\to \mathrm{exp}\left(b\mathrm{ln}\left(a\right)\right)$

 The last transformation is only done if ${ⅇ}^{b\mathrm{ln}\left(a\right)}$ is already present.
 • In all of the previous transformations, i and j denote integers.
 • If no options are specified, all combinations are performed.
 Note: Not all simplifications are valid everywhere. You should be aware of this when calling Combine.

Examples

 > with(SolveTools):
 > Combine(3*x*ln(y)+4*x*ln(z)+exp(t)^5*exp(s)^6);
 ${{ⅇ}}^{{5}{}{t}{+}{6}{}{s}}{+}{x}{}{\mathrm{ln}}{}\left({{y}}^{{3}}{}{{z}}^{{4}}\right)$ (1)
 > Combine(3*x*ln(y)+4*x*ln(z)+exp(t)^5*exp(s)^6,'ln');
 ${\left({{ⅇ}}^{{t}}\right)}^{{5}}{}{\left({{ⅇ}}^{{s}}\right)}^{{6}}{+}{x}{}{\mathrm{ln}}{}\left({{y}}^{{3}}{}{{z}}^{{4}}\right)$ (2)
 > Combine(3*x*ln(y)+4*x*ln(z)+exp(t)^5*exp(s)^6,'exp');
 ${3}{}{x}{}{\mathrm{ln}}{}\left({y}\right){+}{4}{}{x}{}{\mathrm{ln}}{}\left({z}\right){+}{{ⅇ}}^{{5}{}{t}{+}{6}{}{s}}$ (3)
 > Combine((x^y)^5+(x^z)^6+5*t*ln(z)+6*t*ln(x),'power');
 ${{x}}^{{5}{}{y}}{+}{{x}}^{{6}{}{z}}{+}{5}{}{t}{}{\mathrm{ln}}{}\left({z}\right){+}{6}{}{t}{}{\mathrm{ln}}{}\left({x}\right)$ (4)
 > Combine((x^y)^5+(x^z)^6+5*t*ln(z)+6*t*ln(x),'power', 'ln');
 ${{x}}^{{5}{}{y}}{+}{{x}}^{{6}{}{z}}{+}{t}{}{\mathrm{ln}}{}\left({{x}}^{{6}}{}{{z}}^{{5}}\right)$ (5)
 > Combine( a^b+2*exp(b*ln(a)));
 ${3}{}{{ⅇ}}^{{b}{}{\mathrm{ln}}{}\left({a}\right)}$ (6)