Question Number 106996 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}+\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right) \\ $$ Commented by bemath last updated on 10/Aug/20…
Question Number 106888 by bemath last updated on 07/Aug/20 $$@\mathrm{bemath}@ \\ $$$$\mathfrak{g}\mathrm{iven}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{x}\right)}\\{\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{2x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{4x}\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\frac{\pi}{\mathrm{48}}\right)+\mathrm{g}\left(\frac{\pi}{\mathrm{48}}\right)\:. \\ $$ Answered by Dwaipayan Shikari last…
Question Number 172349 by Mikenice last updated on 25/Jun/22 Answered by mr W last updated on 26/Jun/22 $$\mathrm{log}\:\mathrm{3}\:×\left(\mathrm{log}\:\mathrm{3}+\mathrm{log}\:{x}\right)=\mathrm{log}\:\mathrm{4}\:×\left(\mathrm{log}\:\mathrm{4}+\mathrm{log}\:{y}\right) \\ $$$$\mathrm{log}\:\mathrm{4}\:×\mathrm{log}\:{x}=\mathrm{log}\:\mathrm{3}×\mathrm{log}\:{y} \\ $$$${let}\:{X}=\mathrm{log}\:{x},\:{Y}=\mathrm{log}\:{y} \\ $$$${a}=\mathrm{log}\:\mathrm{3},\:{b}=\mathrm{log}\:\mathrm{4} \\…
Question Number 106688 by pticantor last updated on 06/Aug/20 $$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}{z}^{\mathrm{2}{n}−\mathrm{14}} =? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 172190 by Mikenice last updated on 23/Jun/22 Commented by mokys last updated on 23/Jun/22 $${ln}\left({f}\left({x}\right)\right)={cos}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\right)\:{lnx} \\ $$$$ \\ $$$$\frac{{f}\:^{'} \left({x}\right)}{{f}\left({x}\right)}\:=\:\frac{{cos}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\right)}{{x}}\:−\:\left(\mathrm{2}{x}\:+\mathrm{4}\right){sin}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\right){lnx}…
Question Number 172183 by Mikenice last updated on 23/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 172085 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$$\left(\mathrm{3}^{{x}^{\mathrm{3}} −\mathrm{72}{x}+\mathrm{39}} −\mathrm{9}\sqrt{\mathrm{3}}\right)×{log}\left(\mathrm{7}−{x}\right)=\mathrm{0} \\ $$ Answered by mr W last updated on 23/Jun/22 $$\mathrm{log}\:\left(\mathrm{7}−{x}\right)=\mathrm{0}\:\Rightarrow\mathrm{7}−{x}=\mathrm{1}\:\Rightarrow{x}=\mathrm{6}\:…
Question Number 172084 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$$\left(\sqrt{\mathrm{5}+\sqrt{\mathrm{24}}}\right)^{{x}} −\mathrm{10}=\left(\sqrt{\mathrm{5}−\sqrt{\mathrm{24}}}\right)^{{x}} \\ $$ Answered by mr W last updated on 23/Jun/22 $${let}\:{t}=\left(\sqrt{\mathrm{5}+\sqrt{\mathrm{24}}}\right)^{{x}} >\mathrm{0}…
Question Number 172081 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$${log}_{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{5}{x}−\mathrm{1}\right)\underset{−} {>}\mathrm{0} \\ $$ Commented by mr W last updated on 23/Jun/22 $$\mathrm{5}{x}−\mathrm{1}\geqslant\mathrm{1}…
Question Number 172086 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$$\mathrm{2}^{{x}^{\mathrm{2}} } −\mathrm{40}{x}=\mathrm{0} \\ $$ Commented by mr W last updated on 23/Jun/22 $${you}\:{can}\:{only}\:{approximate}!…