how do i simply this eqaution?
You need to use the formula
$\displaystyle \log{x}-\log{y} = \log{\frac{x}{y}}$
$\displaystyle \log_{10}{B^3} - (\log_{10}{AB} - \log_{10}{\frac{A}{B}}) = \log_{10}{B^3} - \log_{10}{\frac{AB}{\frac{A}{B}}}$
$\displaystyle = \log_{10}{B^3} - \log_{10}{B^2}$
$\displaystyle = \log_{10}{\frac{B^3}{B^2}}$
$\displaystyle = \log_{10}{B}$.