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if p^{2} + q^{2} = 23pq, Prove that:

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

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p^{2} + q^{2} = (p + q)^{2} - 2pq

Since p^{2} + q^{2} = 23pq, and p^{2} + q^{2} = (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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