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Category: Logarithms

log-5-x-9-log-5-3x-2-12-log-5-2x-1-0-

Question Number 156109 by cortano last updated on 08/Oct/21 $$\:\:\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{x}−\mathrm{9}}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{2x}−\mathrm{1}}\right)\:\leqslant\:\mathrm{0} \\ $$ Answered by yeti123 last updated on 08/Oct/21 $$\left(\mathrm{1}\right)\:\cap\:\left(\mathrm{2}\right)\:\cap\:\left(\mathrm{3}\right)\:\cap\:\left(\mathrm{4}\right)\:\cap\:\left(\mathrm{5}\right)\:\cap\:\left(\mathrm{6}\right)\:=\:\mathrm{9}\:<\:{x}\:\leqslant\:\mathrm{21478} \\…

log-2-8x-log-3-27x-x-2-x-0-

Question Number 90434 by john santu last updated on 23/Apr/20 $$\frac{\mathrm{log}_{\mathrm{2}} \left(\mathrm{8}{x}\right).\mathrm{log}_{\mathrm{3}} \left(\mathrm{27}{x}\right)}{{x}^{\mathrm{2}} −\mid{x}\mid}\:\leqslant\:\mathrm{0}\: \\ $$ Commented by jagoll last updated on 28/Apr/20 $${how}\:\frac{\mathrm{1}}{\mathrm{8}}\:<\:\frac{\mathrm{1}}{\mathrm{27}}\:?\: \\…

If-y-x-y-2-x-and-dx-x-3y-m-n-log-x-y-2-1-then-m-2n-A-1-B-3-C-5-D-7-

Question Number 89652 by john santu last updated on 18/Apr/20 $$\mathrm{If}\:\left({y}\left({x}−{y}\right)\right)^{\mathrm{2}} \:=\:{x}\:{and}\: \\ $$$$\int\:\frac{{dx}}{\left({x}−\mathrm{3}{y}\right)}\:=\:\left(\frac{{m}}{{n}}\right)\:\mathrm{log}\:\left[\:\left({x}−{y}\right)^{\mathrm{2}} −\mathrm{1}\right] \\ $$$${then}\:{m}+\mathrm{2}{n}\:=\: \\ $$$${A}.\mathrm{1}\:\:\:\:\:{B}.\:\mathrm{3}\:\:\:\:\:\:\:\:{C}.\:\mathrm{5}\:\:\:\:\:\:\:\:\:{D}.\mathrm{7} \\ $$ Terms of Service Privacy…

log-x-6-2-log-1-6-1-x-2-log-1-x-1-6-log-6-x-3-4-0-

Question Number 89456 by jagoll last updated on 17/Apr/20 $$\left(\mathrm{log}_{{x}} \left(\mathrm{6}\right)\right)^{\mathrm{2}} \:+\:\left(\mathrm{log}_{\frac{\mathrm{1}}{\mathrm{6}}} \left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2}} +\: \\ $$$$\mathrm{log}_{\frac{\mathrm{1}}{\:\sqrt{{x}}}} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:+\:\mathrm{log}_{\sqrt{\mathrm{6}}} \:\left({x}\right)\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:=\:\mathrm{0} \\ $$ Answered by john santu last…

x-1-and-x-2-is-root-log-2-x-1-2-log-x-2-the-value-is-x-1-x-2-a-2-1-4-b-2-1-2-c-4-1-4-d-4-1-2-e-6-1-4-

Question Number 154989 by bagjagugum123 last updated on 24/Sep/21 $${x}_{\mathrm{1}} \:{and}\:{x}_{\mathrm{2}} \:{is}\:{root}\:\mathrm{log}_{\mathrm{2}} {x}^{\left(\mathrm{1}+^{\mathrm{2}} \mathrm{log}\:{x}\right)} =\mathrm{2},\:{the}\:{value} \\ $$$${is}\:{x}_{\mathrm{1}} +{x}_{\mathrm{2}} =\:… \\ $$$${a}.\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${b}.\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${c}.\:\mathrm{4}\frac{\mathrm{1}}{\mathrm{4}}…