$$e^x \log _a x+\frac{x^{n-1}}{\log _e a}$$

$$e^x x^{n-1}\left\{x \log _a x+\frac{1}{\log _e a}+n \log _a x\right\}$$

$$n x^{n-1} \log _a x e^x$$

$$x^n \log _a x \cdot e^x$$