In the equation: $$b^b = \frac{1}{256}$$ There is a clear real solution, $b=-4$. Is it possible to find this solution using the lambert W function? This is what I have tried so far: $$ b^b = \frac{1}{256} $$ $$b\ln(b) = -\ln(256)$$ $$\ln(b)e^{\ln(b)} = -\ln(256)$$ $$\ln(b) = W(-\ln(256))$$ $$b = e^{W(-\ln(256))}$$ This is a solution but I want to find the real solution. Is that possible without just guessing?
2026-04-02 15:47:06.1775144826
Is it possible to use the lambert w function to find the real solution to this equation?
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