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Find the value of ((log)3 4)((log)4 5)((...

Find the value of `((log)_3 4)((log)_4 5)((log)_5 6)((log)_6 7)((log)_7 8)((log)_8 9)dot`

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`log_(3)4log_(4)5log_(5)6log_(6)7log_(7)8log_(8)9`
`=(log4)/(log3)xx(log)5/(log4)xx(log6)/(log5)xx(log7)/(log6)xx(log8)/(log7)xx(log9)/(log8)`
`=(log9)/(log3)=log_(3)9=2`
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