If a^p=b^q=c^r=abc, fnd the value of pqr in terms of p,q and r. With steps please.

Question

This is a question from Class 9 Indian Institute of Technology Foundation Series from Trishna

Answer 1

a^p=abc, taking logs to any base: plog(a)=log(abc); p=log(abc)/log(a), q=log(abc)/log(b), r=log(abc)/log(c).

pqr=log³(abc)/(log(a)log(b)log(c)).

pqr in terms of p, q, r is pqr.