Solve the equation `(1-2(2logx)^(2))/(logx-2(logx)^(2))=1`

Explanation

The given equation can rewrite in the form
`(1-2(2logx)^(2))/(logx-2(logx)^(2))=1`
`implies(1-8(logx)^(2))/(logx-2)(logx)^(2))-1=0`
Let `logx=t`
then `(1-8t^(2))/(5-2t^(2))-1=0implies(1-8t^(2)-t+2t^(2))/(t-2t^(2))=0`
`implies(1-t-6t^(2)/((t-2t^(2))=0implies((1+2t)(1-3t))/(t(1-2t))=0`
`implies{(t=-1/2),(t=1/3):}implies{(logx=-1/2),(logx=1/3):}implies{:(x_(1)=10^(-1//2)),(x_(2)=10^(1//3)):}`
Hence `x_(1)=1/(sqrt(10))` and `x_(2)=root(3)(10)` are the roots of the original equation.