You used a natural logarithm on the right side ( $\displaystyle{\ln{{50}}}\usepackage{cmbright}\Huge\$ ), but a common logarithm on the left side $\displaystyle{\left({{\log{{10}}}}^{{{2}{x}-{3}}}={2}{x}-{3}\right)}\usepackage{cmbright}\Huge\$ . You need to use the same type of logarithm on both sides of the equation when solving.