Use l'Hôpital's Rule to find the limit. \[ \lim _{x \rightarrow 0^{+}} \frac{\ln \left(x^{2}+10 x\right)}{\ln x} \]

Step 1 ：Given the function \(\lim _{x \rightarrow 0^{+}} \frac{\ln \left(x^{2}+10 x\right)}{\ln x}\), we need to find the limit as x approaches 0 from the right.

Step 2 ：First, we check if the limit of the original quotient is of the form 0/0 or ∞/∞. If it is, we can apply l'Hôpital's Rule.

Step 3 ：The limit of the numerator as x approaches 0 from the right is negative infinity, and the limit of the denominator as x approaches 0 from the right is also negative infinity. This is the form ∞/∞, so we can apply l'Hôpital's Rule.

Step 4 ：Next, we find the derivatives of the numerator and the denominator. The derivative of the numerator is \(\frac{2x + 10}{x^{2} + 10x}\) and the derivative of the denominator is \(\frac{1}{x}\).

Step 5 ：Then, we find the limit of the quotient of these derivatives as x approaches 0 from the right. The limit is 1.

Step 6 ：Final Answer: The limit of the given function as x approaches 0 from the right is \(\boxed{1}\).