log_{12} 81 = p, then 3[(4-p)/(4+p)] is equal to

- log
_{4}16 - log
_{6}8 - log
_{6}16 - log
_{2}8

### Answer

log_{12} 81 = p

log_{12} 3^{4} = p

4 log_{12} 3 = p

Now,

4 - p = 4 - 4 log_{12} 3

= 4(1 - log_{12} 3)

= 4(log_{12} 12 - log_{12} 3)

= 4 log 4

Similarly,

4 + p = 4 log 36

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

= 3 log_{36} 4

= log_{6} 8

**The correct option is B.**