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Prove that 2log((p+q)/5) = log(p) + log(q)
math log-function
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if p2 + q2 = 23pq, Prove that:

2log((p+q)/5) = log(p) + log(q)

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peter
Asked by peterrep:938
University of Lagos Nigeria
17 June 2020

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peter
Peter answeredrep:938
University of Lagos Nigeria
12 August 2020
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p2 + q2 = (p + q)2 - 2pq

Since p2 + q2 = 23pq, and p2 + q2 = (p + q)2 - 2pq

(p + q)2 - 2pq  = 23pq

(p + q)2 = 2pq + 23pq

(p + q)2 = 25pq

Dividing throug by 25,

(p + q)2/25 = 25pq/25

(p + q)2/25  = pq

((p + q)/25)2 = pq

Multiplying through with log

log((p + q)/25)2 = log(pq)

2log((p + q)/25) = log(p) + log(q)


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