Buktikan limit mendekati tak hingga (log 10x^10-1/x^10-10)=1

Saya nulisnya pakai latex, ya.

[tex]$\begin{align}\lim_{x \to \infty} (\log \frac{10x^{10} - 1}{x^{10}-10})&=\lim_{x \to \infty} (\log \frac{10x^{10}-\frac{x^{10}}{x^{10}}}{x^{10}-10\frac{x^{10}}{x^{10}}})\\ &=\lim_{x \to \infty} (\log(\frac{x^{10}}{x^{10}})\frac{10-\frac{1}{x^{10}}}{1-\frac{10}{x^{10}}}) \\ &=\lim_{x \to \infty} \log(\frac{10-\frac{1}{x^{10}}}{1-\frac{10}{x^{10}}}) \\ &=\log \frac{10-0}{1-0} \\ &=\log 10 \\ &=1\end{align}[/tex]