Re: logx y Message #1 Posted by Tom Sherman on 12 June 2005, 1:35 p.m.
Hi Gerson,
I liked your problem because it made me cut through about 50 years of strata that overlay my schoolboy 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
