Question

$\lim_{x \to \infty} \frac{ln (x+1)}{ln(x)}$

Answer 1

L'Hôpital

$\it \lim\limits_{x \to \infty} \dfrac{ln(x+1)}{lnx} = \lim\limits_{x \to \infty} \dfrac{\dfrac{1}{x+1}}{\dfrac{1}{x}} = \lim\limits_{x \to \infty} \dfrac{1}{x+1}\cdot\dfrac{x}{1} =\lim\limits_{x \to \infty} \dfrac{x+1}{x} =1$