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I'm interested in how the number of operations of $O(x\lg{x})$ algorithms grow over time, I want to find the maximum value of $x$ for different values of $t$, but I can't seem to rearrange the equation in terms of $x$.

William Albuquerque
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  • Try implicit differentiation or use the product logarithm – Тyma Gaidash Sep 12 '23 at 11:46
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    Such equations can only be solved numerically. The Lambert-W function was invented to solve such equations , but it can also not be computed directly like a quadratic equation. – Peter Sep 12 '23 at 11:49
  • Why can it not be computed directly? – William Albuquerque Sep 12 '23 at 13:59
  • It kind of depends on what you (and @Peter who wrote that) mean by "computed directly", I prefer to state it as "can't be expressed with standard functions". But that just leads to the question on what "standard functions" are. I'm not sure any good definition exists, my guideline is that it's functions that can be calculated on a "standard" calculator. – Henrik supports the community Sep 13 '23 at 08:44

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