Take the common logarithm of both sides: $\displaystyle{{\log{{10}}}}^{{{2}{x}-{3}}}={\log{{50}}}\usepackage{cmbright}\Huge\$

Because $\displaystyle{\log}_{{{b}}}{{b}}^{{m}}={m}\usepackage{cmbright}\Huge\$ , the equation simplifies to: $\displaystyle{2}{x}-{3}={\log{{50}}}\usepackage{cmbright}\Huge\$

Solve for x: $\displaystyle{2}{x}={\log{{\left({50}\right)}}}+{3}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}=\frac{{{\log{{\left({50}\right)}}}+{3}}}{{2}}\usepackage{cmbright}\Huge\$

Use a calculator to evaluate the logarithm and find the value of x.

$\displaystyle{x}=\frac{{{\left({1.69897}\ldots\right)}+{3}}}{{2}}=\frac{{{4.69897}\ldots}}{{2}}={2.34948}\ldots\usepackage{cmbright}\Huge\$