Use the quotient property: $\displaystyle{\log}_{{b}}\frac{{M}}{{N}}={\log}_{{b}}{M}-{\log}_{{b}}{N}\usepackage{cmbright}\Huge\$

Then use the product property twice: $\displaystyle{\log}_{{b}}{M}{N}={\log}_{{b}}{M}+{\log}_{{b}}{N}\usepackage{cmbright}\Huge\$

$\displaystyle{\log}_{{{4}}}{\left(\frac{{{64}{x}}}{{{16}{y}}}\right)}={\log}_{{{4}}}{64}{x}-{\log}_{{{4}}}{16}{y}\usepackage{cmbright}\Huge\$

$\displaystyle={\log}_{{{4}}}{64}+{\log}_{{{4}}}{x}-{\left({\log}_{{{4}}}{16}+{\log}_{{{4}}}{y}\right)}={3}+{\log}_{{{4}}}{x}-{2}-{\log}_{{{4}}}{y}\usepackage{cmbright}\Huge\$

$\displaystyle={1}+{\log}_{{{4}}}{x}-{\log}_{{{4}}}{y}\usepackage{cmbright}\Huge\$