$\displaystyle{4}={\log}_{{{b}}}{625}\usepackage{cmbright}\Huge\$ is equivalent to $\displaystyle{{b}}^{{4}}={625}\usepackage{cmbright}\Huge\$ .

Try different bases: $\displaystyle{{2}}^{{4}}={16}\usepackage{cmbright}\Huge\$ , $\displaystyle{{3}}^{{4}}={81}\usepackage{cmbright}\Huge\$ , $\displaystyle{{5}}^{{4}}={625}\usepackage{cmbright}\Huge\$

So $\displaystyle{b}={5}\usepackage{cmbright}\Huge\$ .