I'm reading book called "Prime Obession" which attempts to give a layperson's introduction to the Riemann Hypothesis. In laying the groundwork in one of the early chapters the author is explaining the fact that the function log(x) increases more slowly in total than x raised to any power. For example, log(x) crosses the function x^0.1 somewhere less than e^e, and then falls below it again somewhere in the quadrillions. I'm wondering how one would go about solving the equation to find the Y axis intercepts? I want to find where log(x) = x^0.1, in trying to simplify the problem I end up with log(x)/x = e^0.1, but I'm not able to go any farther. The equation obviously has two solutions, so I imagine there's a polynomial involved somewhere? Any advice would be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# Solving a certain equation involving logarithms

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