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{\bf Question}

Show that the root of $x^2-\log x=\sigma$ where $\sigma$ is a
positive number, behaves like

$$x \sim
\sigma^{\frac{1}{2}}+\ds\frac{1}{4}\sigma^{-\frac{1}{2}}\log\sigma+\cdots,\
\sigma\to +\infty.$$

\vspace{.5in}

{\bf Answer}

See example in lecture notes.


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