Category: Logarithms

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 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 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 40873 by scientist last updated on 28/Jul/18 $${If}\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} =\mathrm{0},\:\:{prove}\:{that}\:\mathrm{log}\:\left({a}+{b}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{log}\:{a}\:+\mathrm{log}\:{b}\:+\mathrm{log}\:\mathrm{3}\right) \\ $$$$\left[{given}\:{a}+{b}\neq\mathrm{0}\right] \\ $$ Answered by math1967 last updated on 29/Jul/18 $${a}^{\mathrm{3}} +{b}^{\mathrm{3}}…

Question Number 106024 by john santu last updated on 02/Aug/20 $$\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{5x}−\mathrm{6}\right).\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{256}\right)=\mathrm{8} \\ $$ Commented by Dwaipayan Shikari last updated on 02/Aug/20 $$\left\{\mathrm{2},\mathrm{3}\right\} \\…