2^^^1.5 = ?

[Daniel]

Sorry if I don't want to fight this war one number at a time. I believe that the most effective approach to the higher hyperoperators for problems like \( 2\uparrow{^k} 1.5 \) is to tackle the issue for all smooth functions \( f^t(x) \). This then gives a solution for tetration, pentation and all higher hyperoperators. 
http://tetration.org/Tetration/index.html

https://www.overleaf.com/read/zjwkzgftsqkm