Correct. Using the Change of Base formula: $\displaystyle{\log}_{{100}}{10},{000}=\frac{{{\log{{10}}},{000}}}{{{\log{{100}}}}}\usepackage{cmbright}\Huge\$

Now $\displaystyle{\log{{10}}},{000}={4}\usepackage{cmbright}\Huge\$ , because $\displaystyle{{10}}^{{4}}={10},{000}\usepackage{cmbright}\Huge\$ , and $\displaystyle{\log{{100}}}={2}\usepackage{cmbright}\Huge\$ , because $\displaystyle{{10}}^{{2}}={100}\usepackage{cmbright}\Huge\$ .

Therefore: $\displaystyle\frac{{{\log{{10}}},{000}}}{{{\log{{100}}}}}=\frac{{4}}{{2}}={2}\usepackage{cmbright}\Huge\$