What is the limit as x approaches infinity of (ln(3x))/x ?

The limit as x approaches infinity of (ln(3x))/x is 0

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limit as x approaches infinity of (ln(3x))/x

x \to \infty lim (\frac{ln ( 3 x )}{x})

0

Solution steps

x \to \infty lim (\frac{ln ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{\frac{1}{x}}{1})

= x \to \infty lim (\frac{\frac{1}{x}}{1})

Simplify

= x \to \infty lim (\frac{1}{x})

Apply Infinity Property:

x \to \infty lim (\frac{c}{x ^{a}}) = 0

= 0

x \to \infty lim ((\frac{x + 7}{x + 3})^{2 x})

x \to 0 lim (sin^{s i n (x)} (x))

x \to 0 + lim (\frac{1}{1 + 2 ^{\frac{1}{x}}})

x \to 5 lim (\frac{- 3}{x - 5})

x \to 2 - lim ((x - 2) \cdot ln (2 - x))

What is the limit as x approaches infinity of (ln(3x))/x ?
The limit as x approaches infinity of (ln(3x))/x is 0