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(52788) (Show Source):
You can put this solution on YOUR website! .
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) = .
