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

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

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

x \to e + lim ((ln (x))^{\frac{1}{x - e}})

e^{\frac{1}{e}}

Decimal

1.44466 \dots

Solution steps

x \to e + lim ((ln (x))^{\frac{1}{x - e}})

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{\frac{1}{e}}

= e^{\frac{1}{e}}

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