Mathematics research

Question

1. Given that log_r pq = m, log_p qr = k and6 log_q pr = n , show that m+n+k=mnk-2

Answer 1

Rewriting the equations in exponential for gives.

(1) pq = r^m

(2) qr = p^k

(3) pr = qⁿ

(1) p = r^m/q

(1) → (2) q^1+k = r^mk-1

(2) → (3) r^m+1 = qⁿ⁺¹

(3) r = q^(n+1)/(m+1)

(3) → (2) q^1+k = q^{(n+1)(mk-1)/(m+1)}

(3) (1+k)(m) = (n+1)(mk-1)

(3) m + n + k = mkn - 2