Question 1125393
.


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

            although it is not stated explicitly.



(a)   show that  {{{(1/2)*(log(p)+log(q))}}}  equals   log {{{((p+q)/sqrt(13)))}}}



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


{{{p^2 + 2pq + q^2}}} = 13pq  ====>


{{{(p+q)^2}}} = 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 {{{((p+q)/(sqrt(13)))}}} = {{{(1/2)*(log(p) + log(q))}}}.
</pre>

QED