Dear Alex,yesterday I came across your page:
https://www.cut-the-knot.org/do_you_know/irrat.shtml
Noone seems to notice the fact that (for example!)
log4 is irrational and sqrt(10) is irrational, but
sqrt(10)^log4=10^log2=2 is rational.
Where is the problem? Or am I wrong?
Kind regards
Chris