What is the limit as x approaches 0+of ln(1/(x^4)) ?

The limit as x approaches 0+of ln(1/(x^4)) is infinity

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limit as x approaches 0+of ln(1/(x^4))

x \to 0 + lim (ln (\frac{1}{x ^{4}}))

\infty

Solution steps

x \to 0 + lim (ln (\frac{1}{x ^{4}}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= x \to 0 + lim (- ln (x^{4}))

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

= - x \to 0 + lim (ln (x^{4}))

ln (x^{4}) = 4 ln (x)

= - x \to 0 + lim (4 ln (x))

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

= - 4 \cdot x \to 0 + lim (ln (x))

Apply the common limit:

x \to 0 + lim (ln (x)) = - \infty

= - 4 (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

What is the limit as x approaches 0+of ln(1/(x^4)) ?
The limit as x approaches 0+of ln(1/(x^4)) is infinity