Evaluate the limit$,$ using L$\text{'}$H$$pital$\text{'}$s Rule if necessary.

$\underset{x}{lim}\frac{ln(x^7)}{x^6}$

Step $1$

The limit to be evaluated is $\underset{x}{lim}\frac{ln(x^7)}{x^6}.$

By direct substitution we have the following.

$\underset{x}{lim}\frac{ln(x^7)}{x^6}=\frac{?}{}\sqrt[\phantom{2}]{}$

Thus, the direct substitution leads to an expression in indeterminate

Step $2$

Apply the property of logarithm, which states the following.

$ln(a^m)=()ln(a)$

Therefore, we get the following.

$\underset{x}{lim}\frac{ln(x^7)}{x^6}=\underset{x}{lim}\frac{ln(x)}{x^6}$