Solve `(log)_(tanx)(2+4cos^2x)=2`

Explanation

`log_("tan x")(2+4 cos^(2) x)=2, tan x gt 0, tan x ne 1`
`rArr 2+4 cos^(2) x=tan^(2) x`
`rArr 3+4 cos^(2) x= sec^(2) x`
`rArr 4 cos^(4) x+3 cos^(2) x-1 =0`
Let `cos^(2) x=t`
`rArr 4t^(2)+3t-1=0`
`rArr (4t-1) (t+1) =0`
`rArr t=1//4 or t=-1`
`rArr cos^(2) x=1/4`
`rArr cos^(2) x="cos"^(2) pi/3`
`rArr x=n pi +pi/3, n in Z" "( :'" for "x=npi - pi/3, tan x lt 0)`