06-12-2005, 01:35 PM

Hi Gerson,

I liked your problem because it made me cut through about 50 years of strata that overlay my school-boy days!

First I had to remind myself why ln(y)/ln(x) equals the logarithm of y to the base x.

Then it became a matter of eliminating that extra x<>y step in getting to ln(y)/ln(x).

Since (x root of y) is the same as y^(1/x), then:

((ln(x)) root of y) = y^(1/ln(x))

And taking logarithms again, ln(y^(1/ln(x))) = ln(y)/ln(x)

It was a bit of a dizzy ride, but much fun. Thanks for setting it up, and for the interesting link.

Cheers, Tom