Substitute 3.0 for R in the formula: $\displaystyle{3.0}={\log{{\left(\frac{{A}}{{A}_{{0}}}\right)}}}\usepackage{cmbright}\Huge\$

Rewrite as an exponential equation: $\displaystyle{{10}}^{{3.0}}=\frac{{A}}{{A}_{{0}}}\usepackage{cmbright}\Huge\$

Multiply both sides by $\displaystyle{A}_{{0}}\usepackage{cmbright}\Huge\$ : $\displaystyle{A}={1},{000}{A}_{{0}}\usepackage{cmbright}\Huge\$