Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. $$ \lim _{x \rightarrow \infty} \frac{\ln (5 x+7)}{\ln (7 x+6)+10} $$

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Calculate the limit $$ \lim _{x\rightarrow \infty} \frac{\ln(5x+7)}{\ln(7x+6)+10} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\ln{\left(5x+7\right)}}{\ln{\left(7x+6\right)}+10}\right)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(\ln{\left(5x+7\right)}\right)}{\frac{d}{dx}\left(\ln{\left(7x+6\right)}+10\right)}\right)$$
- step2: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{5}{5x+7}}{\frac{7}{7x+6}}\right)$$
- step3: Simplify the expression:
  $$\lim _{x\rightarrow +\infty}\left(\frac{5\left(7x+6\right)}{7\left(5x+7\right)}\right)$$
- step4: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(5\left(7x+6\right)\right)}{\frac{d}{dx}\left(7\left(5x+7\right)\right)}\right)$$
- step5: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{35}{35}\right)$$
- step6: Simplify the expression:
  $$\lim _{x\rightarrow +\infty}\left(1\right)$$
- step7: Evaluate:
  $$1$$
The limit of $$ \frac{\ln (5x+7)}{\ln (7x+6)+10} $$ as $$ x $$ approaches infinity is 1.
The limit is 1.

Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

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