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Solve for x: `log_(2)x le 2/(log_(2)x-1)`

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Best answer
Let `log_(2)x=t`
`tle2/(t-1) rArr t-2/(t-1) le0`
`rArr (t^(2)-t-2)/(t-1) le0 rArr ((t-2)(t+1))/(t-1) le0`
`rArr t in (-infty, -1) cup (1,2)`
or `x in (0,1/2) cup (2,4)`

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