evaluate the following in terms of x and y

Question

If log p=x and log q=y, evaluate the following in terms of x and y:

#1)  (log p^-4)/(loq q^-5) = ?

#2) (log p^5)^−3 = ?

Answer 1

(logp^-4) / (logq^-5) = (-4logp) / (-5logq) = -4x / (-5y) = 4x / (5y)

 

(logp⁵)^-3 = (5logp)^-3 = (5x)^-3 = 1 / (5x)³

 

                                            = 1 / (125x³)