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Question Number 172244 by mr W last updated on 24/Jun/22

$$solve$$$$2^{x^2}-40x=0$$$$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by mr W last updated on 24/Jun/22

$$2^{x^2}-40x=0$$$$2^{x^2}=40x>0$$$${\left(2^{x^2}\right)}^2={\left(40x\right)}^2$$$$2^{2x^2}={40}^2{x}^2$$$$-\frac{2\ln 2}{{40}^2}=(-2x^2\ln 2)e^{-2x^2\ln 2}$$$$-2x^2\ln 2=W(-\frac{2\ln 2}{{40}^2})$$$$x^2=-\frac{1}{2\ln 2}W(-\frac{2\ln 2}{{40}^2})$$$$\Rightarrow x=\sqrt{-\frac{1}{2\ln 2}W(-\frac{2\ln 2}{{40}^2})}$$$$=\{\begin{array}{l}\sqrt{-\frac{-9.27886375}{2\ln 2}}=2.587138\\ \sqrt{-\frac{-0.00086718566}{2\ln 2}}=0.025011\end{array}$$

Commented by Tawa11 last updated on 24/Jun/22

$$\mathrm{Great}\mathrm{sir}$$

Commented by peter frank last updated on 27/Jun/22

$$\mathrm{thank}\mathrm{you}$$

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