$\text{ If }{\log }_3\left(x^4-x^3\right)-{\log }_3(x-1)=3\text{ then }x\text{ is equal to ? }$

${\log }_3\left(x^4-x^3\right)-{\log }_3(x-1)=3$

$$\begin{gathered} \Rightarrow {\log }_3\left[\frac{\left(x^4-x^3\right)}{(x-1)}\right]=3\left(\because {\log }_a\frac{m}{n}={\log }_{a}m-{\log }_{a}n\right) \\ \Rightarrow {\log }_3\left[\frac{{\mathrm{x}}^3(\mathrm{x}-1)}{(\mathrm{x}-1)}\right]=3 \\ \Rightarrow {\log }_3{\mathrm{x}}^3=3 \\ \Rightarrow 3{\log }_3\mathrm{x}=3\left(\because {\log }_{\mathrm{a}}{\mathrm{m}}^{\mathrm{n}}={\mathrm{nlog}}_{\mathrm{a}}\mathrm{m}\right) \\ \Rightarrow {\log }_3\mathrm{x}=1\therefore \mathrm{x}=3 \end{gathered}$$