You may have simplified correctly for the first two steps, but then made a mistake with the factor 2. Start with the power property, then the quotient property: $\displaystyle{\log}_{{10}}{{\left(\frac{{{1},{000}}}{{a}}\right)}}^{{2}}={2}\cdot{\log}_{{10}}{\left(\frac{{{1},{000}}}{{a}}\right)}={2}{\left({\log}_{{10}}{1},{000}-{\log}_{{10}}{a}\right)}\usepackage{cmbright}\Huge\$

If you have a term such as $\displaystyle{2}\cdot{\log}_{{{10}}}{a}\usepackage{cmbright}\Huge\$ , you may not rewrite it with the factor 2 inside the logarithm.