How do you solve this logarithmic problem

Solve for x:

16 (log 'base 9' x)^4 - (log 'base 3' x^3)^2 + 8 = 0

16 (log 'base 9' x)^4 - (log 'base 3' x^3)^2 + 8 = 0
16 (log 'base 3'' x / log 'base 3' 9 )^4 - (3log 'base 3' x)^2 + 8 = 0
(log 'base 3'' x )^4 - 9 (log 'base 3' x)^2 + 8 = 0
y^4 - 9y^2 +8 =0
(y^2 - 8) (y^2-1) =0
y = 1, -1
y = 2.828; -2.828
log 'base 3'' x = 1
x =3 ---answer
log 'base 3'' x = -1
x = 3^-1 ---answer
log 'base 3'' x = 2.828
x = 3^ 2.828 ---answer
log 'base 3'' x = - 2.828
x = 3^-2.828 ---answer