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Question Number 172082 by Mikenice last updated on 23/Jun/22

$$solve$$$${log}_{0.5}^{2}x+{log}_{0.5}x-2\underset{-}{<}0$$

Commented by mokys last updated on 23/Jun/22

$${log}_{0.5}^{2}x+{log}_{0.5}x⩽2$$$$2{log}_{0.5}x+{log}_{0.5}x⩽2$$$$3{log}_{0.5}x⩽2$$$${log}_{0.5}x⩽\frac{2}{3}$$$$x⩽{(0.5)}^{\frac{2}{3}}⩽\sqrt[3]{\frac{1}{4}}$$$$$$$$anotherway:$$$$$$$$\frac{lnx}{ln(0.5)}⩽\left(\frac{2}{3}\right)\Rightarrow lnx⩽\left(\frac{2}{3}\right)ln(0.5)$$$$$$$$lnx⩽ln{(0.5)}^{\frac{2}{3}}\Rightarrow x⩽{(0.5)}^{\frac{2}{3}}⩽\sqrt[3]{\frac{1}{4}}$$$$$$$$Aldolaimy$$

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