The correct answer is (B):
log12 81 = p ⇒ log1234 = p
4log12 3=p
⇒ p/4 = log12 3
3(4-p/4+p)=3(1-p/4/1+p/4)
= 3(1-log12 3/log12+log12 3)
= 3(log(12/3)/log(12/3))
= 3log4/log36 = 3log36 4
= log68
Consider two distinct positive numbers \( m, n \) with \( m > n \). Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between \( x \) and \( y \) is -
If \[ \log_{p^{1/2}} y \times \log_{y^{1/2}} p = 16, \] then find the value of the given expression.