What is the limit as x approaches 1+of (x-1)^{ln(x)} ?

The limit as x approaches 1+of (x-1)^{ln(x)} is 1

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limit as x approaches 1+of (x-1)^{ln(x)}

x \to 1 + lim ((x - 1)^{l n (x)})

1

Solution steps

x \to 1 + lim ((x - 1)^{l n (x)})

Apply exponent rules

= x \to 1 + lim (e^{l n (x) l n (x - 1)})

Apply the Limit Chain Rule:

1

= 1

What is the limit as x approaches 1+of (x-1)^{ln(x)} ?
The limit as x approaches 1+of (x-1)^{ln(x)} is 1