l'hopital's rule

• You can deal with indeterminate forms like \(1^\infty\) by taking the log. This is used in finding \(\lim_{n\rightarrow \infty} (1+\frac{1}{n})^n = c\). Taking the log, we get \(\ln c = n \ln (1+\frac{1}{n}) = \frac{\ln(1+\frac{1}{n})}{\frac{1}{n}}\). Now this is in the familiar \(\frac{0}{0}\) indeterminate form.
• source: here