Question 429482
Solution:{{{log(3,(y-2))+log(3,y)=4}}}

Express 4 as logarithm with base 3 : {{{log(3,x)=4}}}=> 3^4=x =>x=81.

{{{log(3,y(y-2))=log(3,81)}}}

y(y-2)=81 Set equation to zero and solve it.

{{{y^2-2y-81=0}}}

{{{y=(2+-sqrt(4+324))/2}}}

The solution is {{{1+sqrt(82)}}}.Approximately 10.

Done.