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) 
~~~~~~~~~~~~~~~~~



            Notice that the condition  ASSUMES   that  p > 0;   q > 0;   and   p > q,

            although it is not stated explicitly.



(a)   show that  {{{(1/2)*(log(p)+log(q))}}}  equals   log((p-q)/3)


<pre>
{{{p^2 + q^2}}} = 11pq  ====>  subtract 2pq from both sides. You will get  ====>


{{{p^2 - 2pq + q^2}}} = 9pq  ====>


{{{(p-q)^2}}} = 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) = {{{(1/2)*(log(p) + log(q))}}}.
</pre>

QED


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Your formula in part &nbsp;(b) &nbsp;is &nbsp;INCORRECT.