Kissing Curves

Stephen ARNOLD
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At exactly what values of a and x do the curves y = a^x and y = log_a(x) kiss?

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Drag the slider to find the value of a when the two curves kiss.
Now try and prove your result algebraically!

a^x = log_a(x) when x =
a^x = log_a(x) when a =

Steve Arnold, with thanks to Mike May S.J. for his JavaScripting. 24/03/2008, Created with GeoGebra