Show $frac{1}{log(x)}$ is in $L^p ( (0,0.5))$ for $p geq 1$ without using the $Li(x)$ function or using $u = log(x)$ substitution (that approach gives an infinite series and is not good for evaluating $x=0$).

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# Show $frac{1}{log(x)}$ is in $L^p ( (0,0.5))$ for $p geq 1$

Show $frac{1}{log(x)}$ is in $L^p ( (0,0.5))$ for $p geq 1$ without using the $Li(x)$ function or using $u = log(x)$ substitution (that approach gives an infinite series and is not good for evaluating $x=0$).

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