What is the limit as x approaches infinity of x^{8/(ln(x))} ?

The limit as x approaches infinity of x^{8/(ln(x))} is e^8

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limit as x approaches infinity of x^{8/(ln(x))}

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

e^{8}

Decimal Notation

2980.95798 \dots

Solution steps

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

Apply exponent rules

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

Multiply

\frac{8}{ln ( x )} ln (x) : 8

= x \to \infty lim (e^{8})

x \to a lim c = c

= e^{8}

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}))

x \to π lim (cos (\frac{x}{2}))

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

What is the limit as x approaches infinity of x^{8/(ln(x))} ?
The limit as x approaches infinity of x^{8/(ln(x))} is e^8