Logarithms

log12 81 = p, then 3[(4-p)/(4+p)] is equal to

  1. log4 16
  2. log6 8
  3. log6 16
  4. log2 8

Answer

log12 81 = p

log12 34 = p

4 log12 3 = p

Now,

4 - p = 4 - 4 log12 3

= 4(1 - log12 3)

= 4(log12 12 - log12 3)

= 4 log 4

Similarly,

4 + p = 4 log 36

3[(4-p)/(4+p)] = 3 log 4 / log 36

= 3 log36 4

= log6 8

The correct option is B.