Question

If `a=log_(24)12,b=log_(36)24, c=log_(48)36`, then show that `1+abc=2bc`
A. 2bc-1
B. 2bc+1
C. bc-1
D. bc+1

Answer 1

Correct Answer - 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`