Question Number 20102 by ajfour last updated on 21/Aug/17 $${Solve}\:{the}\:{equation}: \\ $$$$\left(\mathrm{log}\:_{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\right)^{\mathrm{2}} =\mathrm{1} \\ $$ Answered by allizzwell23 last updated on 21/Aug/17 $$\:\:\mathrm{log}_{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\:=\:\mathrm{1}…
Question Number 85433 by jagoll last updated on 22/Mar/20 $$−\mathrm{log}_{\left(\frac{\mathrm{x}}{\mathrm{6}}\right)} \left(\frac{\mathrm{log}_{\mathrm{10}} \sqrt{\mathrm{6}−\mathrm{x}}}{\mathrm{log}_{\mathrm{10}} \mathrm{x}}\right)\:>\:\mathrm{log}_{\mathrm{10}} \left(\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\right) \\ $$ Answered by jagoll last updated on 22/Mar/20 Terms of…
Question Number 85347 by jagoll last updated on 21/Mar/20 $$\mathrm{log}_{\mathrm{0}.\mathrm{5}} ^{\mathrm{2}} \left(\mathrm{8}+\mathrm{2x}−\mathrm{x}^{\mathrm{2}} \right)−\mathrm{7log}_{\mathrm{2}} \left(\mathrm{8}+\mathrm{2x}−\mathrm{x}^{\mathrm{2}} \right)<−\mathrm{12} \\ $$ Commented by john santu last updated on 21/Mar/20…
Question Number 150641 by maged last updated on 14/Aug/21 $$\mathrm{1}+\sqrt{\mathrm{3}^{\mathrm{x}} }=\mathrm{2}^{\mathrm{x}} \\ $$$$\mathrm{x}=? \\ $$ Commented by amin96 last updated on 14/Aug/21 $$\sqrt{\mathrm{3}^{{x}} }=\mathrm{3}^{{m}} \:\:\:\:\mathrm{3}^{{x}}…
Question Number 84986 by jagoll last updated on 18/Mar/20 $$\mathrm{5}^{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{\mathrm{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2x}+\mathrm{3}} \: \\ $$ Commented by mr W last updated on 18/Mar/20…
Question Number 84828 by john santu last updated on 17/Mar/20 $$\mathrm{log}_{\mathrm{3}} \left(\mathrm{25x}^{\mathrm{2}} −\mathrm{4}\right)−\mathrm{log}_{\mathrm{3}} \left(\mathrm{x}\right)\:\leqslant\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{26x}^{\mathrm{2}} +\frac{\mathrm{17}}{\mathrm{x}}−\mathrm{10}\right) \\ $$ Commented by john santu last updated on…
Question Number 84826 by jagoll last updated on 16/Mar/20 $$\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}}\:+\:\mathrm{log}_{\mathrm{3}} \:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10}}\:=\:\mathrm{2} \\ $$ Commented by john santu last updated on 16/Mar/20 $$\mathrm{x}\:=\:\mathrm{1} \\…
Question Number 84674 by jagoll last updated on 15/Mar/20 $$\frac{\mathrm{6}−\mathrm{log}_{\mathrm{16}} \:\left(\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{3}+\mathrm{2log}_{\mathrm{16}} \left(\mathrm{x}^{\mathrm{2}} \right)}\:<\:\mathrm{2} \\ $$ Commented by jagoll last updated on 15/Mar/20 $$\left(\mathrm{i}\right)\:\mathrm{x}\:\neq\:\mathrm{0}\: \\…
Question Number 84459 by jagoll last updated on 13/Mar/20 $$\begin{cases}{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\frac{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\mathrm{8log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{3}}\\{\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)+\frac{\mathrm{8log}_{\mathrm{10}} \left(\mathrm{x}\right)−\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{0}}\end{cases} \\…
Question Number 84051 by john santu last updated on 09/Mar/20 $$\frac{\mathrm{log}_{\left({x}−\mathrm{1}\right)} \:\left(\mathrm{6}{x}−\mathrm{1}\right)}{\left(\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} \right)\right)^{\mathrm{3}} −\mathrm{log}_{\mathrm{3}} \:\left({x}\right)\right)\left(\mathrm{log}_{\mathrm{3}} \:\left({x}−\mathrm{2}\right)−\mathrm{1}\right)}\:\geqslant\:\mathrm{0} \\ $$ Answered by john santu last updated…