User blog comment:Nayuta Ito/generalization of arrow notation/@comment-10429372-20141025122001

I think that 3 ^^ 1.5 should be 3^ ( 3 ^^ 0.5 ), where k = 3 ^^ 0.5 the number k is such that k^k = 3.

This would make 3 ^^ 1.5 = 3^ ( 3 ^^ 0.5 ) ~ 3^ ( 1.825455 ) ~ 7.25