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

• 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.