The Change of Base formula is $\displaystyle{\log}_{{{b}}}{x}=\frac{{{\log}_{{{a}}}{x}}}{{{\log}_{{{a}}}{b}}}\usepackage{cmbright}\Huge\$ , not $\displaystyle{\log}_{{{b}}}{x}={\log}_{{{a}}}{b}\cdot{\log}_{{{a}}}{x}\usepackage{cmbright}\Huge\$ .