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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
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$\lim_{x\to\infty }\left(e^{\frac{1}{\ln\left(x\right)}\ln\left(\frac{1}{x}\right)}\right)$
Learn how to solve problems step by step online. Find the limit of (1/x)^(1/ln(x)) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(\frac{1}{x}\right). Simplify the logarithm \ln\left(\frac{1}{x}\right). Simplify the fraction \frac{-\ln\left(x\right)}{\ln\left(x\right)} by \ln\left(x\right).