What is the limit as x approaches infinity of (ln(x))^{3/x} ?

The limit as x approaches infinity of (ln(x))^{3/x} is 1

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limit as x approaches infinity of (ln(x))^{3/x}

x \to \infty lim ((ln (x))^{\frac{3}{x}})

1

Solution steps

x \to \infty lim ((ln (x))^{\frac{3}{x}})

Apply exponent rules

= x \to \infty lim (e^{\frac{3}{x} l n (l n (x))})

Apply the Limit Chain Rule:

1

= 1

x \to a lim ([f (x) + g (x)])

x \to \infty lim (x^{\frac{8}{l n ( x )}})

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

x \to - 3 - lim (\frac{x + 1}{∣ x ∣})

x \to \infty lim (arccos (1 - 3^{- x}))

What is the limit as x approaches infinity of (ln(x))^{3/x} ?
The limit as x approaches infinity of (ln(x))^{3/x} is 1