# 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 $$x=0$$).