Question Number 15452 by 1415403730 last updated on 10/Jun/17 Answered by mrW1 last updated on 11/Jun/17 $$\mathrm{MN}=\mathrm{P} \\ $$$$\mathrm{N}=\mathrm{M}^{−\mathrm{1}} \mathrm{P} \\ $$$$\mathrm{M}=\left(_{\mathrm{4}\:\:\:\mathrm{3}} ^{\mathrm{1}\:\:\:\mathrm{2}} \right) \\…
Question Number 80844 by jagoll last updated on 07/Feb/20 $${If}\:\left(\mathrm{log}_{\mathrm{10}} \left({ax}\right)\right)\left(\mathrm{log}_{\mathrm{10}} \left({bx}\right)\right)=−\mathrm{1} \\ $$$${find}\:{x}\:{in}\:{term}\:{a}\:{and}\:{b}\: \\ $$ Commented by jagoll last updated on 07/Feb/20 $${can}\:{anyone}\:{help}\:{me} \\…
Question Number 15184 by Tinkutara last updated on 08/Jun/17 $$\mathrm{If}\:{y}\:=\:\mathrm{ln}\:{x}\:\mathrm{and}\:{y}\:=\:{a}^{{x}} \:\mathrm{have}\:\mathrm{a}\:\mathrm{solution} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$$$\left(\mathrm{1}\right)\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$$$\left(\mathrm{2}\right)\:\left(\frac{\mathrm{1}}{{e}},\:{e}\right) \\ $$$$\left(\mathrm{3}\right)\:\left(\mathrm{1},\:{e}\right) \\ $$$$\left(\mathrm{4}\right)\:\left(\mathrm{0},\:\mathrm{1}\right] \\ $$ Commented by…
Question Number 80687 by Power last updated on 05/Feb/20 Commented by Power last updated on 05/Feb/20 $$\left.\mathrm{a}\left.\right)\left.\frac{\mathrm{1}}{\mathrm{6}}\left.\:\:\:\:\:\mathrm{b}\right)\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\mathrm{c}\right)\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\mathrm{d}\right)\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented by MJS last updated on…
Question Number 15097 by Tinkutara last updated on 07/Jun/17 $$\mathrm{If}\:\mathrm{log}_{\mathrm{4}} \:\mathrm{log}_{\frac{\mathrm{1}}{\mathrm{2}}} \:\mathrm{log}_{\mathrm{3}} \:\left({x}\right)\:>\:\mathrm{0}\:\mathrm{then}\:{x}\:\mathrm{belongs} \\ $$$$\mathrm{to}\:\left(\mathrm{1},\:{a}\right),\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}^{\mathrm{2}} \:\mathrm{is}? \\ $$ Commented by prakash jain last updated on…
Question Number 145829 by bramlexs22 last updated on 08/Jul/21 Answered by EDWIN88 last updated on 08/Jul/21 $$\left(\mathrm{1}\right)\sqrt{{x}+\frac{\mathrm{15}}{\mathrm{4}}}\:\neq\:\mathrm{1}\:;\:{x}\neq\:−\frac{\mathrm{11}}{\mathrm{4}} \\ $$$$\:\:{and}\:{x}\:>−\frac{\mathrm{15}}{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{8}}{\mathrm{3}}{x}\right)>\mathrm{0}\Rightarrow{x}\left({x}−\frac{\mathrm{8}}{\mathrm{3}}\right)>\mathrm{0} \\ $$$$\Rightarrow{x}<\mathrm{0}\:\cup\:{x}>\frac{\mathrm{8}}{\mathrm{3}} \\…
Question Number 14702 by tawa tawa last updated on 03/Jun/17 Answered by mrW1 last updated on 03/Jun/17 $$\left(\mathrm{sin}\:\mathrm{6}°+\:{i}\:\mathrm{cos}\:\mathrm{6}°\right)^{\mathrm{30}} \\ $$$$=\left(\mathrm{cos}\:\mathrm{84}°+\:{i}\:\mathrm{sin}\:\mathrm{94}°\right)^{\mathrm{30}} \\ $$$$=\mathrm{cos}\:\mathrm{30}×\mathrm{84}°+\:{i}\:\mathrm{sin}\:\mathrm{30}×\mathrm{84}°\: \\ $$$$=\mathrm{cos}\:\mathrm{2529}°+\:{i}\:\mathrm{sin}\:\mathrm{2520}°\: \\…
Question Number 14701 by tawa tawa last updated on 03/Jun/17 Commented by mrW1 last updated on 03/Jun/17 $${I}\:{think}\:{none}\:{of}\:{the}\:{answers}\:{is}\:{right}. \\ $$$${xy}=\mathrm{20}^{\mathrm{1}} =\mathrm{20} \\ $$$${x}+{y}=\mathrm{5}^{\mathrm{2}} =\mathrm{25} \\…
Question Number 145524 by physicstutes last updated on 05/Jul/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{argument}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{below} \\ $$$$\left(\mathrm{i}\right)\:{z}\:=\:\mathrm{1}+{e}^{\frac{\pi}{\mathrm{6}}{i}} \\ $$$$\left(\mathrm{ii}\right)\:{z}\:=\:\mathrm{1}\:−{e}^{\frac{\pi}{\mathrm{6}}{i}} \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\left({i}\right)\:{z}\:=\:\mathrm{1}+{e}^{{i}\frac{\pi}{\mathrm{6}}} \\…
Question Number 14404 by Nysiroke last updated on 31/May/17 $${solve}\:{for}\:{x}\:{and}\:{y}\:{in} \\ $$$$ \\ $$$${x}^{{y}^{{y}} } ={log}\mathrm{8} \\ $$$${x}^{{x}^{{x}} } ={log}\mathrm{3} \\ $$ Commented by prakash…