Question Number 206303 by ayietaamos last updated on 11/Apr/24 $${log}_{\mathrm{2}} \mathrm{4} \\ $$ Answered by MATHEMATICSAM last updated on 11/Apr/24 $$\mathrm{log}_{\mathrm{2}} \mathrm{4} \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{2}}…
Question Number 205496 by cortano12 last updated on 22/Mar/24 Answered by Frix last updated on 22/Mar/24 $${x}>\mathrm{0} \\ $$$${t}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{1}+{t}\right)\:=\mathrm{3log}_{\mathrm{7}} \:{x} \\ $$$$\mathrm{Obviously}\:{t}=\mathrm{7}…
Question Number 204300 by depressiveshrek last updated on 11/Feb/24 $${x}^{\mathrm{2}} \mathrm{log}_{\mathrm{3}} {x}^{\mathrm{2}} −\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\mathrm{log}_{\mathrm{9}} \left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3log}_{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}{x}+\mathrm{3}}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 11/Feb/24…
Question Number 204174 by patrice last updated on 08/Feb/24 Answered by Faetmaaa last updated on 27/Feb/24 $$\left.\mathrm{3}\right)- \\ $$$$\forall{n}\in\boldsymbol{\mathrm{N}}^{\bigstar} \\ $$$${S}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{ln}\left(\frac{{k}}{{n}}\right) \\…
Question Number 203375 by a.lgnaoui last updated on 17/Jan/24 $$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$ Commented by mr W last updated on 18/Jan/24 $$\mathrm{17}\:\mathrm{sin}\:\mathrm{5}{x}+\mathrm{17}\:\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\mathrm{13} \\ $$$$\mathrm{sin}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\frac{\mathrm{13}}{\mathrm{17}}…
Question Number 202172 by MATHEMATICSAM last updated on 22/Dec/23 $$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{18}\:=\:\mathrm{A}\:\mathrm{and}\:\mathrm{log}_{\mathrm{24}} \mathrm{54}\:=\:\mathrm{B}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{AB}\:+\:\mathrm{5}\left(\mathrm{A}\:−\:\mathrm{B}\right)\:=\:\mathrm{1}. \\ $$ Answered by Rasheed.Sindhi last updated on 22/Dec/23 $$\mathrm{12}^{\mathrm{A}} =\mathrm{18}\:\&\:\mathrm{24}^{\mathrm{B}}…
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Question Number 200224 by cortano12 last updated on 15/Nov/23 Answered by Rasheed.Sindhi last updated on 16/Nov/23 $$\begin{cases}{{yx}^{\mathrm{log}_{{y}} {x}\:} ={x}^{\frac{\mathrm{5}}{\mathrm{2}}} ……………\left({i}\right)}\\{\mathrm{log}_{\mathrm{4}} {y}.\mathrm{log}_{{y}} \left({y}−\mathrm{3}{x}\right)=\mathrm{1}…\left({ii}\right)\:\:}\end{cases} \\ $$$$\left({ii}\right)\Rightarrow\:\frac{\mathrm{1}}{\mathrm{log}_{{y}} \mathrm{4}\:}=\frac{\mathrm{1}}{\mathrm{log}_{{y}}…
Question Number 199956 by cortano12 last updated on 11/Nov/23 Answered by Frix last updated on 11/Nov/23 $$\left(\mathrm{1}\right)\:\Rightarrow\:{x}={y}\left({y}^{\mathrm{2}} +{y}+\mathrm{2}\right)\wedge{y}>\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\Rightarrow\:\frac{{x}}{{y}}=\mathrm{4}\vee\frac{{x}}{{y}}=\mathrm{8} \\ $$$$\Rightarrow \\ $$$${x}=\mathrm{4}\wedge{y}=\mathrm{1}\:\vee\:{x}=\mathrm{16}\wedge{y}=\mathrm{2} \\…