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Find the value of log(2) (1/(7^(log(7)...

Find the value of ` log_(2) (1/(7^(log_(7) 0.125)))`.

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The correct Answer is:
3
` log_(2)(1/(7^(log_(2)(2sqrt3)))+2/(log_(3)(2sqrt3)))^(2)=(4log_((2sqrt3))2+ 2log_((2sqrt3))3)^(2)`
`= (log_(2sqrt3)16+log_(2sqrt3)9)^(2)`
` = (log_(2sqrt3)144)^(2)`
` (log_(2sqrt3)(2sqrt3)^(4))^(2)`
` = 4^(2) = 16`
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