What is the limit as x approaches infinity of (ln(x^5))/(13x) ?

The limit as x approaches infinity of (ln(x^5))/(13x) is 0

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limit as x approaches infinity of (ln(x^5))/(13x)

x \to \infty lim (\frac{ln ( x ^{5} )}{13 x})

0

Solution steps

x \to \infty lim (\frac{ln ( x ^{5} )}{13 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{13} \cdot x \to \infty lim (\frac{ln ( x ^{5} )}{x})

ln (x^{5}) = 5 ln (x)

= \frac{1}{13} \cdot x \to \infty lim (\frac{5 ln ( x )}{x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{ln ( x )}{x})

Apply L'Hopital's Rule

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

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{\frac{1}{x}}{1})

Simplify

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{1}{x})

Apply Infinity Property:

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

= \frac{1}{13} \cdot 5 \cdot 0

Simplify

\frac{1}{13} \cdot 5 \cdot 0 : 0

= 0

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What is the limit as x approaches infinity of (ln(x^5))/(13x) ?
The limit as x approaches infinity of (ln(x^5))/(13x) is 0