What is the limit as x approaches 3-of ln|x-3| ?

The limit as x approaches 3-of ln|x-3| is -infinity

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limit as x approaches 3-of ln|x-3|

x \to 3 - lim (ln ∣ x - 3 ∣)

- \infty

Solution steps

x \to 3 - lim (ln ∣ x - 3 ∣)

x - 3

is negative when

x \to 3 -

. Therefore

∣ x - 3 ∣ = - x + 3

= x \to 3 - lim (ln (- x + 3))

Apply the Limit Chain Rule:

- \infty

= - \infty

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x \to 0 lim (x^{2} - 7 x + 10)

x \to 0 lim (\frac{ln ( ln ( x ) )}{x})

x \to \infty lim (4 + \frac{7}{x})

What is the limit as x approaches 3-of ln|x-3| ?
The limit as x approaches 3-of ln|x-3| is -infinity