+- Tetration Forum (https://tetrationforum.org)
+-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3)
+--- Thread: Conjecture on semi-exp base change [2015] (/showthread.php?tid=971)
Conjecture on semi-exp base change [2015] - tommy1729 - 03/24/2015
Let x,y > 0.
Let B>b>2.
Expb is exp base b and expB is exp base B.
Analogue for ln.
Conjecture :
A(x,y) = expB^[1/2](lnB^[1/2](x) + lnB^[1/2](y))
B(x,y) = expb^[1/2](lnb^[1/2](x) + lnb^[1/2](y))
C(x,y) = (2+x^2+y^2)^(B-b)
A(x,y)/( B(x,y) ln(2+C(x,y)) ) < 2
Regards
Tommy1729