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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$
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$\lim_{x\to\infty }\left(\ln\left(\frac{7x}{x+2}\right)\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of ln(7x)-ln(x+2) 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. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions.