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Let a= log(3) 20, b = log(4) 15 and c =...

Let `a= log_(3) 20, b = log_(4) 15 and c = log_(5) 12`. Then find the value of `1/(a+1)+1/(b+1)+1/(c+1)`.

Text Solution

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We have
`a+1 = log_(3) 20 + log_(3) 3 = log_(3) 60`
` b+ 1 = log_(4) 15 + log_(4) 4 = log_(4) 60`
` c+1 = log_(5) 12+ log_(5) 5 = log_(5) 60`
`1/(a+1)+1/(b+1)+1/(c+1)=1/(log_(3) 60)+1/(log_(4)60)+1/(log_(5)60)`
` =log_(60)3+log_(60)4+log_(60)5`
` = log_(60)(3 xx 4 xx 5)`
` = log_(60) 60`
` = 1`
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