What is the limit as x approaches 2 of x/(ln(x-1)) ?

The limit as x approaches 2 of x/(ln(x-1)) is diverges

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limit as x approaches 2 of x/(ln(x-1))

x \to 2 lim (\frac{x}{ln ( x - 1 )})

diverges

Solution steps

x \to 2 lim (\frac{x}{ln ( x - 1 )})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 2 + lim (\frac{x}{ln ( x - 1 )}) = \infty

x \to 2 - lim (\frac{x}{ln ( x - 1 )}) = - \infty

= diverges

What is the limit as x approaches 2 of x/(ln(x-1)) ?
The limit as x approaches 2 of x/(ln(x-1)) is diverges