SOLUTION: Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals: (a) log((p+q)/√13)

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Question 1125393: Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals:
(a) log((p+q)/√13)
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            Notice that the condition  ASSUMES  that  p > 0;  q > 0,
            although it is not stated explicitly.


(a)   show that    equals  log 


 = 11pq  ====>  add 2pq to both sides. You will get  ====>


 = 13pq  ====>


 = 13pq  ====>  take the logarithm from both sides ====>


2*log(p+q) = log(13) + log(p) + log(q)


2*log(p+q) - log(13) = log(p) + log(q)


2*(log(p+q) - 2*log(sqrt(13))) = log(p) + log(q)


log  = .

QED


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