Correct. Take the common logarithm of both sides: $\displaystyle{{\log{{10}}}}^{{{6}{x}-{3}}}={\log{{1}}},{000}\usepackage{cmbright}\Huge\$

Because $\displaystyle{\log}_{{{b}}}{{b}}^{{m}}={m}\usepackage{cmbright}\Huge\$ , the equation simplifies to: $\displaystyle{6}{x}-{3}={\log{{1}}},{000}\usepackage{cmbright}\Huge\$

The value of $\displaystyle{\log{{1}}},{000}\usepackage{cmbright}\Huge\$ is 3, so the equation becomes: $\displaystyle{6}{x}-{3}={3}\usepackage{cmbright}\Huge\$

Solve the linear equation: $\displaystyle{6}{x}={6}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={1}\usepackage{cmbright}\Huge\$