Question Number 208503 by efronzo1 last updated on 17/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 208412 by efronzo1 last updated on 15/Jun/24 Answered by A5T last updated on 15/Jun/24 $$\mathrm{8}=\mathrm{24}^{\frac{\mathrm{1}}{{a}}} ,\mathrm{27}=\mathrm{24}^{\frac{\mathrm{1}}{{b}}} ,\mathrm{64}=\mathrm{24}^{\frac{\mathrm{1}}{{c}}} \\ $$$$\Rightarrow\mathrm{24}^{\mathrm{3}} =\mathrm{8}×\mathrm{27}×\mathrm{64}=\mathrm{24}^{\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\frac{{ab}+{bc}+{ca}}{{abc}}\right)} \\ $$$$\Rightarrow\frac{{ab}+{bc}+{ca}}{{abc}}=\mathrm{3}\Rightarrow\frac{\mathrm{2022}{abc}}{{ab}+{bc}+{ca}}=\mathrm{2022}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{674} \\…
Question Number 208384 by efronzo1 last updated on 14/Jun/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by A5T last updated on 14/Jun/24 $${log}_{{abc}} \left({a}\right)+{log}_{{abc}} \left({b}\right)=\mathrm{2}+\mathrm{3}=\mathrm{5}\Rightarrow{log}_{{abc}} \left({ab}\right)=\mathrm{5} \\ $$$${log}_{{abc}}…
Question Number 208322 by alcohol last updated on 11/Jun/24 Answered by Berbere last updated on 11/Jun/24 $$\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}}\right)^{{k}} =\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\frac{\left(\mathrm{1}+{k}\right)^{{k}} }{{k}^{{k}} }=\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}}…
Question Number 208139 by efronzo1 last updated on 06/Jun/24 $$\:\:\:\: \\ $$ Answered by Ghisom last updated on 06/Jun/24 $${x}>\mathrm{0} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{5}\:+\mathrm{ln}\:\mathrm{2}}=\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\frac{\mathrm{ln}\:\left({x}^{\mathrm{2}}…
Question Number 208083 by nachosam last updated on 04/Jun/24 $$\int_{\left[\mathrm{0},\infty\right]} \left(\frac{\mathrm{1}}{{x}}\right)^{{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$ Answered by Saiki last updated on 04/Jun/24 Answered by…
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) \\…