Question 1069845
{{{log(8,(xy))=3}}}
{{{xy=8^3}}}
{{{xy=512}}}
.
.
.
{{{log(2,(x))*log(2,(y))=18}}}
{{{log(2,(x))*log(2,(512/x))=18}}}
{{{log(2,(x))*(log(2,(512))-log(2,(x)))=18}}}
{{{log(2,(x))*(9-log(2,(x)))=18}}}
Use a substitution,
{{{u=log(2,(x))}}}
{{{u(9-u)=18}}}
{{{-u^2+9u-18=0}}}
{{{u^2-9u+18=0}}}
{{{(u-3)(u-6)=0}}}
Two "u" solutions,
{{{u-3=0}}}
{{{u=3}}}
and
{{{u-6=0}}}
{{{u=6}}}
So,
{{{log(2,(x))=3}}}
{{{x=2^3}}}
{{{x=8}}}
and
{{{log(2,(x))=6}}}
{{{x=2^6}}}
{{{x=64}}}
So
{{{x=8}}},{{{y=512/8=64}}}
and
{{{x=64}}},{{{y=512/64=8}}}