Match the following List I to List II

Answer

`atoq; btos; c to p; d to r`

Explanation

a. We have `1/(log_(3)pi)+1/(log_(4)pi)=log_(pi)3+log_(pi)4=log_(pi) 12`
But ` pi^(2) lt12lt pi^(3)," we have " 2 lt log_(pi) 12 lt 3`.
b. ` 3^(a) = 4, a = log_(3) 4`
Similarly, ` b = log_(4) 5 ` etc.
Hence,
`abcdef=log_(3) 4* log_(4) 5* log_(5) 6* log_(6) 7* log_(7) 8* log_(8) 9`
` = log_(3) 9 = 2`
c. We have to find characteristic of ` log_(2) 2008`.
We know that ` log_(2) 1024 = 10 and log_(2) 2048 = 11`, therefore
` 10 lt log_(2) 2008 lt 11`
Hence, it has characteristic is 10.
d. ` log_(2)(log_(2)(log_(3) x)) = 0`
` rArr log_(2)(log_(3)x) = 1`
` rArr log_(3)x = 2`
` rArr x = 9`
Similarly, we have ` log_(3)(log_(2)y) = 1`
` rArr log_(2) y = 3 or y = 8`
Therefore, x - y = 1.