Evaluate : (1)/(log(a)bc + 1) + (1)/(l...

Evaluate :
`(1)/(log_(a)bc + 1) + (1)/(log_(b)ca + 1) + (1)/(log_(c) ab + 1)`

A

0

B

1

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
`(1)/("log"_(a)bc_(+1)) + (1)/("log"_(b)ca_(+1)) +(1)/("log"_(c)ab_(+1))`
`=(1)/("log"_(a)bc + "log"_(a)a) + (1)/("log"_(b)ca + "log"_(b)b) + (1)/("log"_(c)ab + "log"_(c)c)`
`=(1)/("log"_(a)abc) +(1)/("log"_(b)abc) + (1)/("log"_(c)abc)`
` = "log"_(abc) a + "log"_(abc) b + "log"_(abc) c = "log"_(abc)abc = 1`

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