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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given that: p²+q²=11pq, where p and q are constants, show that ½(logp+logq) equals: (a) log((p+q)/√13)      Log On


   

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) About Me  (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  %281%2F2%29%2A%28log%28p%29%2Blog%28q%29%29  equals  log %28%28p%2Bq%29%2Fsqrt%2813%29%29%29 


p%5E2+%2B+q%5E2 = 11pq  ====>  add 2pq to both sides. You will get  ====>


p%5E2+%2B+2pq+%2B+q%5E2 = 13pq  ====>


%28p%2Bq%29%5E2 = 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 %28%28p%2Bq%29%2F%28sqrt%2813%29%29%29 = %281%2F2%29%2A%28log%28p%29+%2B+log%28q%29%29.

QED