Question Number 95108 by bobhans last updated on 23/May/20 $$\mid\mathrm{1}−\mathrm{log}\:_{\left(\frac{\mathrm{1}}{\mathrm{6}}\right)} \left(\mathrm{x}\right)\mid\:+\mathrm{2}\:=\:\mid\mathrm{3}\:−\mathrm{log}\:_{\left(\frac{\mathrm{1}}{\mathrm{6}}\right)} \left(\mathrm{3}\right)\mid\: \\ $$ Answered by john santu last updated on 23/May/20 $$\mathrm{let}\:\mathrm{1}+\mathrm{log}\:_{\mathrm{6}} \left(\mathrm{x}\right)\:=\:\mathrm{t}\: \\…
Question Number 160426 by alf123 last updated on 29/Nov/21 Commented by mr W last updated on 29/Nov/21 $${one}\:{equation}\:{for}\:{two}\:{unknowns} \\ $$$$\Rightarrow{no}\:{unique}\:{solution}! \\ $$ Commented by Rasheed.Sindhi…
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Question Number 159762 by cortano last updated on 21/Nov/21 $$\:\:\:{Given}\:\mathrm{log}\:_{\mathrm{3}} \left({n}\right)=\:\mathrm{log}\:_{\mathrm{6}} \left({m}\right)=\mathrm{log}\:_{\mathrm{12}} \left({m}+{n}\right) \\ $$$$\:\:\:\frac{{m}}{{n}}\:=\:? \\ $$ Answered by bobhans last updated on 21/Nov/21 $$\:\mathrm{log}\:_{\mathrm{3}}…
Question Number 159639 by bobhans last updated on 19/Nov/21 $$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{x}−\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{9}−\mathrm{3}^{\mathrm{x}} \right)−\mathrm{3}}\:\leqslant\:\mathrm{1}\: \\ $$ Answered by tounghoungko last updated on 19/Nov/21 $$\:\:\:\frac{{x}−\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{9}−\mathrm{3}^{{x}} \right)−\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{27}\right)}\:\leqslant\:\mathrm{1}\:;\:\mathrm{9}−\mathrm{3}^{{x}}…
Question Number 159507 by cortano last updated on 18/Nov/21 Commented by tounghoungko last updated on 18/Nov/21 $$\:\frac{\mathrm{5}.\mathrm{5}^{−\mathrm{2}{x}} +\mathrm{5}^{\mathrm{3}} .\mathrm{5}^{−\mathrm{2}{x}} }{\frac{\mathrm{5}}{\mathrm{8}}.\mathrm{2}^{\mathrm{2}{x}} }\:=\:\mathrm{4} \\ $$$$\Leftrightarrow\:\mathrm{5}^{−\mathrm{2}{x}} +\mathrm{5}^{\mathrm{2}} .\mathrm{5}^{−\mathrm{2}{x}}…
Question Number 93957 by O Predador last updated on 16/May/20 $$\: \\ $$$$\:\mathrm{log}_{\sqrt{\mathrm{17}}−\sqrt{\mathrm{2}}} \left(\frac{\mathrm{15}}{\:\sqrt{\mathrm{19}+\sqrt{\mathrm{136}}}}\right)\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{log}_{\sqrt{\mathrm{19}}−\sqrt{\mathrm{3}}} \left(\frac{\mathrm{1}}{\mathrm{22}−\sqrt{\mathrm{228}}}\right)\mathrm{x}\:=\:\mathrm{3} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$ Commented by PRITHWISH…
Question Number 93847 by i jagooll last updated on 15/May/20 $$\mathrm{log}\:_{\mathrm{5}} \:\left(\mathrm{x}−\mathrm{2}\right)+\mathrm{log}\:_{\mathrm{8}} \:\left(\mathrm{x}−\mathrm{4}\right)=\:\mathrm{log}\:_{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right) \\ $$ Commented by john santu last updated on 15/May/20 $$…
Question Number 159157 by physicstutes last updated on 13/Nov/21 Answered by mr W last updated on 13/Nov/21 Commented by mr W last updated on 13/Nov/21…
Question Number 159122 by physicstutes last updated on 13/Nov/21 $$\mathrm{In}\:\mathrm{order}\:\mathrm{to}\:\mathrm{monitor}\:\mathrm{buses}\:\mathrm{in}\:\mathrm{a}\:\mathrm{travel} \\ $$$$\mathrm{agency},\:\mathrm{the}\:\mathrm{manager}\:\mathrm{decides}\:\mathrm{to}\:\mathrm{monitor} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{break}\:\mathrm{downs}\:\mathrm{of}\:\mathrm{the}\:\mathrm{buses} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{sequence}\:\left\{{x}_{{n}} \right\}\:\mathrm{defined}\:\mathrm{by} \\ $$$${x}_{{n}+\mathrm{1}} \:=\:\mathrm{1}.\mathrm{05}\:{x}_{{n}} \:+\:\mathrm{4}.\:\mathrm{Given}\:\mathrm{that}\:{x}_{\mathrm{0}} \:=\:\mathrm{40}. \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{break}\:\mathrm{downs}\:\mathrm{by}\:\mathrm{the}\:\mathrm{buses} \\…