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If a,b,c are consecutive positive intege...

If `a`,`b`,`c` are consecutive positive integers and `log(1+ac)=2K` then the value of `K`

Text Solution

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Let, `b = n`
Then, `a = n-1 and c = n+1`
`=> ac = (n-1)(n+1) = n^2-1`
`:. log(1+ac) = log(1+n^2-1) = logn^2`
`=2logn = 2logb`
We are given,
`log(1+ac) = 2K`
`:. 2logb =2K => K = logb`
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