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Monday 23 February 2004 at 8:10 pm | In Articles | Post Comment

Prove that 2^{\ln3}=3^{\ln2}
The proof should show you how this generalises. If you have studied group theory you can extend this even further by showing that \left(\mathbb{R}^{+}-\left\{1\right\},\circ\right), where \circ is defined by \begin{displaymath} x\circ y=x^{\ln y}\end{displaymath}, is an abelian group.
Why can’t 1 be an element of this group?

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