Substitute the value 50,000 in the formula: $\displaystyle{50},{000}={25},{000}{{e}}^{{{0.03}{t}}}\usepackage{cmbright}\Huge\$

Divide both sides by 25,000: $\displaystyle{2}={{e}}^{{{0.03}{t}}}\usepackage{cmbright}\Huge\$

Take logarithms of both sides of the equation: $\displaystyle{\ln{{2}}}={{\ln{{e}}}}^{{{0.03}{t}}}\usepackage{cmbright}\Huge\$

Because $\displaystyle{\log}_{{{b}}}{{b}}^{{m}}={m}\usepackage{cmbright}\Huge\$ , we have $\displaystyle{{\ln{{e}}}}^{{{0.03}{t}}}={0.03}{t}\usepackage{cmbright}\Huge\$ , and therefore $\displaystyle{\ln{{2}}}={0.03}{t}.\usepackage{cmbright}\Huge\$

Divide both sides by 0.03 to find t: $\displaystyle{t}=\frac{{\ln{{2}}}}{{0.03}}\usepackage{cmbright}\Huge\$