Question 824341
 Given that {{{log(7,(x^2)) = p}}} and {{{log(7,(xy^2)) = q}}}, find {{{log(7,(root(3,xy)))}}} in terms of p and q.
<pre>
{{{log(7,(x^2)) = p}}}        {{{log(7,(xy^2)) = q}}}
 {{{2log(7,(x)) = p}}}       {{{log(7,(x))+log(7,(y^2))=q}}}
{{{log(7,(x)) = p/2}}}         {{{log(7,(x))+2log(7,y)=q}}}
             
                    {{{p/2+2log(7,y)=q}}}
                    {{{p+4log(7,y)=2q}}}
                    {{{4log(7,y)=2q-p}}}
                    {{{log(7,y)=(2q-p)/4}}}

We want to find:

{{{log(7,(root(3,xy))))}}} =
{{{matrix(2,1,"",log(7,((xy)^(1/3)))))}}} =
{{{expr(1/3)log(7,(xy))}}} =
{{{expr(1/3)(log(7,(x))+log(7,(y)))}}} =
{{{expr(1/3)(p/2+(2q-p)/4)}}} =
{{{expr(1/3)(2p/4+(2q-p)/4)}}} =
{{{expr(1/3)((2p+2q-p)/4))}}} =
{{{expr(1/3)((p+2q)/4))}}} =
{{{(p+2q)/12}}}
 
Edwin</pre>