SOLUTION: Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals: (a) log((p-q)/3) (b) log((p+q)/√3)

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Question 1124556: Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals:
(a) log((p-q)/3)
(b) log((p+q)/√3)
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
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Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals:
(a) log((p-q)/3)
(b) log((p+q)/√3)
~~~~~~~~~~~~~~~~~


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


(a)   show that    equals  log((p-q)/3) 

 = 11pq  ====>  subtract 2pq from both sides. You will get  ====>


 = 9pq  ====>


 = 9pq  ====>  take the logarithm from both sides ====>


2*log(p-q) = log(9) + log(p) + log(q)


2*log(p-q) - log(3^2) = log(p) + log(q)


2*(log(p-q) - log(3)) = log(p) + log(q)


log((p-q)/3) = .

QED

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Your formula in part  (b)  is  INCORRECT.


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