Solve the equation:
`log_(x)^(3)10-6log_(x)^(2)10+11log_(x)10-6=0`

Explanation

`Put log_(x)10=t` in the given equation we get
`t^(3)-6t^(2)+11t-6=0implies(t-1)(t-2)(t-3)=0`
then `{(t=1),(t=2),(t=3):}`
It follows that
`{(log_(x)10=1),(log_(x)10=2),(log_(x)10=3):}implies{(x=10),(x^(2)=10),(x^(3)=10):}implies{(x=10),(x=sqrt(10)),(x=root(3)(10)):} [ :' xgt0` and `!=`]
`[:' xgt0 "and" !=1]` ltrbgt `:.x_(1)=10,x_(2)=sqrt(10)` and `x_(3)=root(3)(10)` are the roots of the original equation.`