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Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp
#2
Lots of ideas however mostly not working, for example:

Ivars Wrote:3_log(a^b) =3_log(a[3]b)= 3_log(a)*3_log(b) = 3_log(a)[2]3_log(b)

Assume there would be a function with

Then surely


So if there is an with we have
.
for we also have:

and both together we get


If we assume that is continuous then this is valid not only for rationals but also for reals :
.

No let constant and let be variable:



So for some constant . But then:


if :

which can not be satisfied for all , .

Hence either or which we excluded in our previous considerations.

Proposition. Let be a continuous function defined on the positive reals such that for all , then either for all or for all .
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Messages In This Thread
only identity maps powers to products - by bo198214 - 06/01/2008, 03:01 PM

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