Learn how to solve problems step by step online. Find the limit of ln(3x)-ln(x+9) as x approaches infinity. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). The limit of a logarithm is equal to the logarithm of the limit. If we directly evaluate the limit \lim_{x\to\infty }\left(\frac{3x}{x+9}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.

Find the limit of ln(3x)-ln(x+9) as x approaches infinity