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# Solving for Intersection of Exponentials and Quadratics

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I have one math problem I can't figure out how to do for the life of me. I used Desmos, which gave me an answer to 3 decimal places, but I would like to know about the answer in radical form. Please help!

\(\textrm{When is }f(x)>g(x)?\\ f(x)=2^{x}\\ g(x)=1000x^{2}\)

Jan 24, 2018

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You need to know about a more advanced function called the LambertW function to solve this in terms of radicals etc.

The result, together with a numerical approximation, is as follows:

Jan 24, 2018