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Question Number 153950 by liberty last updated on 12/Sep/21

Answered by EDWIN88 last updated on 13/Sep/21

$$\log {}_{\mid x-\frac{7}{4}\mid }\left(\log {}_{\frac{1}{2}}x\right)⩽0$$$$\Rightarrow \log {}_{\mid x-\frac{7}{4}\mid }\left(\log {}_{\frac{1}{2}}x\right)⩽\log {}_{\mid x-\frac{7}{4}\mid }\left(1\right)$$$$\Rightarrow (\log {}_{\frac{1}{2}}x-1)(\mid x-\frac{7}{4}\mid -1)⩽0$$$$\Rightarrow (2x-1)(\frac{1}{2}-1)(x-\frac{3}{4})(x-\frac{11}{4})⩽0$$$$\Rightarrow (2x-1)(x-\frac{3}{4})(x-\frac{11}{4})⩾0$$$$\Rightarrow \frac{1}{2}<x⩽\frac{3}{4}\cup x⩾\frac{11}{4}$$$$domain0<x<1;x\ne \frac{3}{4};x\ne \frac{11}{4}$$$$\Rightarrow x\in (\frac{1}{2},\frac{3}{4})$$

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