Correct. Take the common logarithm of both sides: $\displaystyle{{\log{{10}}}}^{{{3}{x}-{13}}}={\log{{100}}},{000}\usepackage{cmbright}\Huge\$

Because $\displaystyle{\log}_{{{b}}}{{b}}^{{m}}={m}\usepackage{cmbright}\Huge\$ , the equation simplifies to: $\displaystyle{3}{x}-{13}={\log{{100}}},{000}\usepackage{cmbright}\Huge\$

The value of $\displaystyle{\log{{100}}},{000}\usepackage{cmbright}\Huge\$ is 5, so the equation becomes: $\displaystyle{3}{x}-{13}={5}\usepackage{cmbright}\Huge\$

Solve the linear equation: $\displaystyle{3}{x}={18}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={6}\usepackage{cmbright}\Huge\$