What is the limit as x approaches 0+of (2^x-1)^x ?

The limit as x approaches 0+of (2^x-1)^x is 1

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limit as x approaches 0+of (2^x-1)^x

x \to 0 + lim ((2^{x} - 1)^{x})

1

Solution steps

x \to 0 + lim ((2^{x} - 1)^{x})

Apply exponent rules

= x \to 0 + lim (e^{x l n (2^{x} - 1)})

Apply the Limit Chain Rule:

1

= 1

What is the limit as x approaches 0+of (2^x-1)^x ?
The limit as x approaches 0+of (2^x-1)^x is 1