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Find the value of log(2) (2root(3)9-2) ...

Find the value of ` log_(2) (2root(3)9-2) + log_(2)(12root(3)3+4+4root(3)9)`.

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`log_(2)(2root(3)9-2)+log_(2)(12root(3)3+4+4root(3)9)`
`=log_(2)((72)^(1//3)-(8)^(1//3)))+log_(2)((72)^(2//3)+(8)^(2//3)+(72)^(1//3)(8)^(1//3))`
`=log_(2)((72)^(1//3)-(8)^(1//3)))((72)^(2//3)+(8)^(2//3)+(72)^(1//3)(8)^(1//3))`
`= log_(2)(72-8)`
` = log_(2)64=6`
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