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log-0-2-x-2-4-x-8-x-5-0-




Question Number 81039 by jagoll last updated on 09/Feb/20
((log_( 0,2) (x−2))/((4^x −8)(∣x∣−5))) ≥ 0
$$\frac{\mathrm{log}_{\:\mathrm{0},\mathrm{2}} \left({x}−\mathrm{2}\right)}{\left(\mathrm{4}^{{x}} −\mathrm{8}\right)\left(\mid{x}\mid−\mathrm{5}\right)}\:\geqslant\:\mathrm{0} \\ $$
Commented by john santu last updated on 09/Feb/20
⇒(i) x>2 ∧x≠5   (ii) 4^x −8>0  (iii) (((0,2−1)(x−2−1))/(x−5)) ≥0  ((x−3)/(x−5)) ≤0 ⇒ x∈ [3 ,5) is solution
$$\Rightarrow\left({i}\right)\:{x}>\mathrm{2}\:\wedge{x}\neq\mathrm{5}\: \\ $$$$\left({ii}\right)\:\mathrm{4}^{{x}} −\mathrm{8}>\mathrm{0} \\ $$$$\left({iii}\right)\:\frac{\left(\mathrm{0},\mathrm{2}−\mathrm{1}\right)\left({x}−\mathrm{2}−\mathrm{1}\right)}{{x}−\mathrm{5}}\:\geqslant\mathrm{0} \\ $$$$\frac{{x}−\mathrm{3}}{{x}−\mathrm{5}}\:\leqslant\mathrm{0}\:\Rightarrow\:{x}\in\:\left[\mathrm{3}\:,\mathrm{5}\right)\:{is}\:{solution} \\ $$
Commented by jagoll last updated on 09/Feb/20
thanks you mister
$${thanks}\:{you}\:{mister} \\ $$

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