What is the limit as x approaches 1-of (x-5)/(ln(x)) ?

The limit as x approaches 1-of (x-5)/(ln(x)) is infinity

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limit as x approaches 1-of (x-5)/(ln(x))

x \to 1 - lim (\frac{x - 5}{ln ( x )})

\infty

Solution steps

x \to 1 - lim (\frac{x - 5}{ln ( x )})

\frac{x - 5}{ln ( x )} = (x - 5) \frac{1}{ln ( x )}

= x \to 1 - lim ((x - 5) \frac{1}{ln ( x )})

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

With the exception of indeterminate form

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

x \to 1 - lim (x - 5) = - 4

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

= (- 4) (- \infty)

Apply Infinity Property:

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

= \infty

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What is the limit as x approaches 1-of (x-5)/(ln(x)) ?
The limit as x approaches 1-of (x-5)/(ln(x)) is infinity