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 $${you}\:{can}\:{only}\:{approximate}!…
Question Number 172077 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$${log}_{\mathrm{4}} \left({x}+\mathrm{12}\right).{logx}^{\mathrm{2}} =\mathrm{1} \\ $$ Commented by mr W last updated on 24/Jun/22 $$\mathrm{log}\:\left({x}+\mathrm{12}\right)\mathrm{log}\:{x}^{\mathrm{2}}…
Question Number 172082 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$${log}_{\mathrm{0}.\mathrm{5}} ^{\mathrm{2}} {x}+{log}_{\mathrm{0}.\mathrm{5}} {x}−\mathrm{2}\underset{−} {<}\mathrm{0} \\ $$ Commented by mokys last updated on 23/Jun/22…
Question Number 172078 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Jun/22 $$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$$$\mathrm{2}{logx}={log}\left(\mathrm{5}{x}−\mathrm{4}\right) \\…
Question Number 172076 by Mikenice last updated on 23/Jun/22 $${solve} \\ $$$${log}\left(\mathrm{64}\sqrt[{\mathrm{24}}]{\mathrm{2}^{{x}^{\mathrm{2}} −\mathrm{40}{x}} }\right)=\mathrm{0} \\ $$ Answered by puissant last updated on 23/Jun/22 $$\Rightarrow{log}\mathrm{64}+\frac{\mathrm{1}}{\mathrm{24}}\left({x}^{\mathrm{2}} −\mathrm{40}{x}\right){log}\mathrm{2}=\mathrm{0}…
Question Number 172074 by Mikenice last updated on 23/Jun/22 $${solve}: \\ $$$$\mathrm{5}^{{logx}} =\mathrm{50}−{x}^{{log}\mathrm{5}} \\ $$ Answered by aleks041103 last updated on 23/Jun/22 $$\mathrm{5}^{{logx}} =\mathrm{10}^{{log}\mathrm{5}\:{logx}} =\left(\mathrm{10}^{{logx}}…
Question Number 172028 by Mikenice last updated on 23/Jun/22 $${solve}: \\ $$$$\frac{{log}_{\mathrm{2}} \left(\mathrm{9}−\mathrm{2}^{\left.{x}\right)} \right.}{{log}_{\mathrm{2}} \mathrm{2}^{\left(\mathrm{3}−{x}\right)} }={log}_{\mathrm{2}} \mathrm{2} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 171990 by Mikenice last updated on 22/Jun/22 $${solve}: \\ $$$${log}_{\mathrm{7}} \mathrm{2}\:+\:{log}_{\mathrm{49}} {x}\:={log}_{\mathrm{7}} \sqrt{\mathrm{3}} \\ $$ Answered by nurtani last updated on 23/Jun/22 $$\Leftrightarrow\:{log}_{\mathrm{7}}…