Question Number 41797 by Tawa1 last updated on 12/Aug/18 $$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\:\:\mathrm{48log}_{\mathrm{a}} \mathrm{4}\:\:+\:\:\mathrm{5log}_{\mathrm{4}} \mathrm{a}\:\:=\:\:\frac{\mathrm{a}}{\mathrm{8}} \\ $$ Answered by alex041103 last updated on 13/Aug/18 $${log}_{{b}} {a}=\frac{{lna}}{{lnb}}\:{and}\:{log}_{{a}} {b}=\frac{{lnb}}{{lna}} \\…
Question Number 107318 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\mathrm{6}^{\mathrm{log}\:_{\left({x}−\mathrm{1}\right)} \left(\frac{\mathrm{20}−\mathrm{12}{x}}{{x}−\mathrm{7}}\right)} −\mathrm{36}\:>\mathrm{0} \\ $$ Answered by bobhans last updated on 10/Aug/20 $$\:\:\:\:\:\:\:\:\:\circledast\mathcal{BOBHANS}\circledast \\…
Question Number 107304 by bemath last updated on 10/Aug/20 $$\:\:\:\curlyvee{bemath}\curlyvee \\ $$$$\left(\mathrm{1}\right){Find}\:{domain}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\sqrt{\mathrm{log}\:_{\mathrm{0}.\mathrm{2}} \left(\frac{{x}+\mathrm{2}}{{x}−\mathrm{1}}\right)−\mathrm{1}}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{9}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)−\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)}{\mathrm{sin}\:\left(\mathrm{2018}\pi+\mathrm{4}{x}\right)}=? \\ $$ Answered by bobhans last…
Question Number 107153 by bemath last updated on 09/Aug/20 $$\:\:\:\:\:\:@{bemath}@ \\ $$$$\left(\frac{\mathrm{14}}{\mathrm{5}}\right)^{\frac{\mathrm{28}}{\:\sqrt{{x}}}−\mathrm{5}} =\:\left(\frac{\mathrm{5}}{\mathrm{14}}\right)^{\frac{\mathrm{5}}{\:\sqrt{{x}}}−\mathrm{160}} \\ $$ Answered by bobhans last updated on 09/Aug/20 $$\:\:\:\:\:\:\:\varepsilon\mathrm{bobhans}\varepsilon \\ $$$$\left(\frac{\mathrm{14}}{\mathrm{5}}\right)^{\frac{\mathrm{28}}{\:\sqrt{\mathrm{x}}}−\mathrm{5}}…
Question Number 172601 by Mikenice last updated on 29/Jun/22 Answered by Rasheed.Sindhi last updated on 30/Jun/22 $$\bullet\mathrm{log}_{\mathrm{2}} \left(\frac{\mathrm{75}}{\mathrm{16}}\right)−\mathrm{log}_{\mathrm{2}} \left[\frac{\left(\frac{\mathrm{25}}{\mathrm{81}}\right)^{\mathrm{3}/\mathrm{4}} \left(\frac{\mathrm{25}}{\mathrm{81}}\right)^{\mathrm{1}/\mathrm{4}} }{\left(\frac{\mathrm{125}}{\mathrm{405}}\right)^{\mathrm{1}/\mathrm{2}} }\right]^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{15}}…
Question Number 106996 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\:\:@{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}…