Question 1072646
Written better,  {{{log(9,(xy^2))=(1/2)log(3,x)+log(3,y)}}}


Start with left hand side.


{{{log(3,(xy^2))/log(3,9)}}}


{{{(log(3,x)+log(3,y^2))/log(3,(3^2))}}}


{{{(log(3,x)+2*log(3,y))/(2*log(3,3))}}}


{{{(log(3,x)+2*log(3,y))/(2*1)}}}


{{{(log(3,x)+2*log(3,y))/2}}}


{{{log(3,x)/2+(2/2)log(3,y)}}}


Same as RHS

DONE