If a=log(24)12,b=log(48)36 and c=log(36)...

If `a=log_(24)12,b=log_(48)36` and `c=log_(36)24`, abc is equal to

A

2bc-1

B

2bc+1

C

bc-1

D

bc+1

Text Solution

Verified by Experts

The correct Answer is:

A

We have,
`a = "log"_(24) 12, b= "log"_(36)24 " and " c = "log"_(48) 36`
`rArr abc = "log"_(48) 12 " and " bc = "log"_(48)24`
`rArr abc - 2bc = "log"_(48) 12 -2"log"_(48) 24`
`rArr abc -2bc = "log"_(48) 12 - "log"_(48) 24^(2)`
`rArr abc - 2bc = "log"_(48) ((12)/(24^(2))) = "log"_(48)((1)/(48)) = -"log"_(48) = -1`
`rArr abc = 2bc-1`

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