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Category: Logarithms

If-y-ln-x-and-y-a-x-have-a-solution-then-find-the-range-of-a-1-0-1-2-1-e-e-3-1-e-4-0-1-

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-80687

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…

If-log-4-log-1-2-log-3-x-gt-0-then-x-belongs-to-1-a-then-the-value-of-a-2-is-

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-145829

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-14702

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}°\: \\…

What-is-the-argument-of-the-complex-numbers-below-i-z-1-e-pi-6-i-ii-z-1-e-pi-6-i-

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}}} \\…

original-length-of-the-iron-rod-175-65-increase-6-1-3-175-65-19-3-1-100-175-65-19-175-65-3-100-3337-35-300-11-1245-new-length-original-length-increased-length-175-65-11-1245

Question Number 145437 by Saiki last updated on 04/Jul/21 $${original}\:{length}\:{of}\:{the}\:{iron}\:{rod}=\mathrm{175}.\mathrm{65} \\ $$$$\%\:{increase}=\mathrm{6}\frac{\mathrm{1}}{\mathrm{3}}\%×\mathrm{175}.\mathrm{65} \\ $$$$=\frac{\mathrm{19}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{100}}×\mathrm{175}.\mathrm{65} \\ $$$$=\frac{\mathrm{19}×\mathrm{175}.\mathrm{65}}{\mathrm{3}×\mathrm{100}}=\frac{\mathrm{3337}.\mathrm{35}}{\mathrm{300}}=\mathrm{11}.\mathrm{1245} \\ $$$${new}\:{length}={original}\:{length}+{increased}\:{length} \\ $$$$=\mathrm{175}.\mathrm{65}+\mathrm{11}.\mathrm{1245} \\ $$$$=\mathrm{186}.\mathrm{7745}{cm} \\ $$$${solution}\:{by}\:{CASIO}….. \\…