x power(1/3) -x power(1/9) =64.solve x?

Question

maths

Answer 1

I think you have to use Log, like this:

Log (x^1/3)-Log(x^1/9)=log 64

Using the properties of Log

1/3 log x - 1/9 log x = log 64
log x(1/3-1/9) = log 64

8/9 log x = log 64

x= (e^log 64)/(8/9)

x=64/(8/3)
x=(64*3)/8
x=24

Answer 2

If you put x^1/9 =z you get z^3-z=64
z^3-z-64=0 which has the only real root=4.083321 (scientific calculator)so x=
=315,588.8858