inequality - How to show without calculator that $leftlfloor, log_{10}{999^{999}}rightrfloor =leftlfloor, log_{10}{999^{999}}+log_{10}2rightrfloor$

By wolfram alpha, I get

$\left\lfloor\, \log_{10}{999^{999}}\right\rfloor =\left\lfloor\, \log_{10}{999^{999}}+\log_{10}2\right\rfloor=2996$.

How to prove that $\left\lfloor\, \log_{10}{999^{999}}\right\rfloor =\left\lfloor\, \log_{10}{999^{999}}+\log_{10}2\right\rfloor$ without calculator or wolfram alpha?

Thank in advances.