<PRE><B>Question 478251</B>
1. {{{a/b+b/a=(a^2+b^2)/(ab)}}}
2. {{{log ((a+b) /3) =(1/2) * (log a + log b)}}} multiply both sides by 2
{{{2log ((a+b) /3) = (log a + log b)}}}
Use {{{loga+logb=log((ab))}}}, {{{log(a/b)=loga-logb}}},{{{ n*loga=log(a^n)}}}
{{{log(((a+b)/3)^2)=log((ab))}}}
{{{log((a+b)^2/9)=log((ab))}}}
{{{log((a^2+2ab+b^2))-log9-log((ab))=0}}}
{{{log((a^2+2ab+b^2)/ab)=log9}}}
{{{(a^2+b^2)/ab+(2ab)/ab=9}}}
{{{(a^2+b^2)/ab+2=9}}}
{{{(a^2+b^2)/ab=7}}}</PRE>