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Question Number 27321 by 803jaideep@gmail.com last updated on 05/Jan/18

Commented by 803jaideep@gmail.com last updated on 05/Jan/18

$$\mathrm{plz}\mathrm{solve}\mathrm{it}$$

Answered by mrW1 last updated on 05/Jan/18

$$x>0$$$$\Rightarrow \mid x\mid =x$$$${\log }_{0.5}x=\mid x\mid$$$$\Rightarrow \frac{\ln x}{\ln 0.5}=x$$$$\frac{\ln x}{-\ln 2}=x=e^{\ln x}$$$$(-\ln x)e^{-\ln x}=\ln 2$$$$\Rightarrow -\ln x=W\left(\ln 2\right)$$$$\Rightarrow \frac{1}{x}=e^{W\left(\ln 2\right)}=\frac{\ln 2}{W\left(\ln 2\right)}$$$$\Rightarrow x=\frac{W\left(\ln 2\right)}{\ln 2}=\frac{W(0.639)}{0.639}=\frac{0.444436}{0.639}=0.641$$

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