Question 977136
{{{log(8,xy)=3}}}
=> {{{8^3 = xy}}} ----(i)
Also,
{{{log(2,x) * log (2,y) =18}}}
=>{{{log(2,x)*log(2,512/x)=18}}} (using (i))
=> {{{log(2,x)*(log(2,512)-log(2,x))=18}}}
=> {{{log(2,x)*(log(2,2^9)-log(2,x))=18}}}
=> {{{log(2,x)*(9*log(2,2)-log(2,x))=18}}}
=> {{{log(2,x)*(9*1-log(2,x))=18}}}
Taking {{{log(2,x)}}} as p,
{{{p*(9-p)=18}}}
=> {{{p^2-9p+18 = 0}}}
=> {{{(p-3)(p-6)=0}}}
=> {{{ p=3}}} or {{{p=6}}}
So,
{{{log(2,x) = 3}}} or {{{log(2,x) = 6}}}
=> {{{x=2^3}}} or {{{x=2^6}}}
=> {{{x=8}}} or {{{x=64}}}
=> {{{y=64}}} or {{{y=8}}} (Using eqn. (i))
So the answer sets of x and y are (8,64) or (64,8)