symbol: get rid of assign/unassign (for performance and other reasons).

[ginac.git] / doc / powerlaws.tex

diff --git a/doc/powerlaws.tex b/doc/powerlaws.tex
index 1943957ac0e4b38564e1ada165f68616ecacc410..ade0547d048a51f65f414c08416a3979ea885ee8 100644 (file)
--- a/doc/powerlaws.tex
+++ b/doc/powerlaws.tex
@@ -151,7 +151,19 @@ Hence
 & = & x^{ab} \mbox{ q.e.d.}
 \end{eqnarray}
 
-proof contributed by Adam Strzebonski from Wolfram Research
-({\tt adams@wolfram.com}) in newsgroup {\tt sci.math.symbolic}.
+Proof contributed by Adam Strzebonski ({\tt adams@wolfram.com}) from
+Wolfram Research in newsgroup {\tt sci.math.symbolic}.
 
-\end{document}
\ No newline at end of file
+\subsubsection{$x$ positive, $a$ real and $b$ arbitrary complex}
+We have
+\begin{equation}
+(x^a)^b = e^{b\log e^{a\log x}}.
+\end{equation}
+Because $a$ is real and $x$ is positive, $a\log x$ is real. From this
+it follows that $\log e^{a\log x} = a\log x$. I.e, we see that
+\begin{equation}
+(x^a)^b = e^{ba\log x} = x^{ab}.
+\end{equation}
+Qed.
+
+\end{document}