Substitute the value 300,000 in the formula: $\displaystyle{300},{000}={100},{000}\cdot{{10}}^{{{0.02}{t}}}\usepackage{cmbright}\Huge\$

Divide both sides by 100,000: $\displaystyle{3}={{10}}^{{{0.02}{t}}}\usepackage{cmbright}\Huge\$

Take logarithms of both sides of the equation: $\displaystyle{\log{{3}}}={{\log{{10}}}}^{{{0.02}{t}}}\usepackage{cmbright}\Huge\$

Because $\displaystyle{\log}_{{{b}}}{{b}}^{{m}}={m}\usepackage{cmbright}\Huge\$ , we have $\displaystyle{{\log{{10}}}}^{{{0.02}{t}}}={0.02}{t}\usepackage{cmbright}\Huge\$ , and therefore $\displaystyle{\log{{3}}}={0.02}{t}.\usepackage{cmbright}\Huge\$

Divide both sides by 0.02 to find t: $\displaystyle{t}=\frac{{\log{{3}}}}{{0.02}}\usepackage{cmbright}\Huge\$