x^(2ln(x)-1) +e^1/9=(1+e^1/9) *x^(ln9x)-0.5)
By the "just looking-at-it Theorem" the equation has a solution for x=1
Check:
LS = 1^(2(0)-1 + e^(1/9)
= 1 + e^(1/9
RS = (1+e^(1/9)(1^(ln9 - .5)
but 1^(anything) = 1
= (1 + e^(1/9)(1)
= LS
so x = 1