You may have correctly used the quotient rule to get

$\displaystyle{\log}_{{{3}}}{\left(\frac{{{243}{x}}}{{{27}{y}}}\right)}={\log}_{{{3}}}{243}{x}-{\log}_{{{3}}}{27}{y}\usepackage{cmbright}\Huge\$ , and then used the product rule. But you probably forgot to distribute the minus sign when rewriting $\displaystyle{\log}_{{3}}{27}{y}\usepackage{cmbright}\Huge\$ as $\displaystyle{\log}_{{{3}}}{27}+{\log}_{{{3}}}{y}\usepackage{cmbright}\Huge\$ .