$\log_{10}\left(\dfrac{50}{147}\right) = \log_{10} 2 + 2\log_{10} 5 - \log_{10} 3 - 2\log_{10} ?$

Since $\dfrac{50}{147} = \dfrac{2\cdot 5^2}{3\cdot 7^2}$, expanding gives $\log 2 + 2\log 5 - \log 3 - 2\log 7$. Hence the missing term is $7$.