Question Number 222697 by gabthemathguy25 last updated on 05/Jul/25 Answered by gregori last updated on 05/Jul/25 $$\:\sqrt[{\mathrm{3}}]{{e}^{\mathrm{2ln}\:\left(\mathrm{81}\right)} }\:=\:\left(\mathrm{81}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\:\mathrm{9}^{\frac{\mathrm{4}}{\mathrm{3}}} \\ $$$$\:\sqrt[{\mathrm{4}}]{\left(\mathrm{3}^{\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{9}^{\mathrm{2}} \right)} \right)^{\mathrm{2}} }\:=\:\sqrt{\mathrm{9}}=\:\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 222679 by fantastic last updated on 04/Jul/25 $${If}\:{x}=\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}{x}\:{then}\:\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} {x}}…+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} {x}}=?? \\ $$ Answered by Tawa11 last updated on 04/Jul/25…
Question Number 222104 by efronzo1 last updated on 17/Jun/25 $$\:\:\:\:\mathrm{log}\:_{\mathrm{4}} \:\mathrm{x}\:−\:\mathrm{log}\:_{\mathrm{x}^{\mathrm{2}} } \:\mathrm{8}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:=?\: \\ $$ Answered by mr W last updated on 17/Jun/25…
Question Number 222007 by klipto last updated on 14/Jun/25 $$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$ Commented by AntonCWX8 last updated on 15/Jun/25 $${Do}\:{you}\:{mean}\:{to}\:{find}\:{a}\:{close}\:{form}?…
Question Number 221896 by fantastic last updated on 12/Jun/25 $${If}\:\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a}\:,{then}\:\mathrm{log}\underset{\mathrm{10}} {\:}\left(\frac{\mathrm{1}}{\mathrm{70}}\right)=? \\ $$ Answered by fantastic last updated on 12/Jun/25 $$\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a} \\ $$$$\:{so}\:\mathrm{10}^{{a}}…
Question Number 221853 by fantastic last updated on 11/Jun/25 $${find}\:{x}\:{where} \\ $$$$\mathrm{log}\underset{\mathrm{8}} {\:}{x}−\mathrm{log}\underset{\mathrm{4}} {\:}{x}−\mathrm{log}\underset{\mathrm{2}} {\:}{x}=\mathrm{11} \\ $$ Commented by Tawa11 last updated on 11/Jun/25 $$\mathrm{log}_{\mathrm{2}^{\mathrm{3}}…
Question Number 221869 by fantastic last updated on 12/Jun/25 $${if}\:{a}^{\mathrm{3}−{x}} .{b}^{\mathrm{5}{x}} ={a}^{\mathrm{5}+{x}} .{b}^{\mathrm{3}{x}} \:{then}\:{show}\:{that} \\ $$$${x}\mathrm{log}\:\left(\frac{{b}}{{a}}\right)=\mathrm{log}\:{a} \\ $$ Answered by fantastic last updated on 12/Jun/25…
Question Number 221760 by OmoloyeMichael last updated on 09/Jun/25 Answered by shunmisaki007 last updated on 09/Jun/25 $$\left(\mathrm{For}\:{x}>\mathrm{0}\:\mathrm{and}\:{x}\neq\mathrm{1}.\right) \\ $$$$\mathrm{log}_{{x}} \left(\frac{\mathrm{log}_{\mathrm{4}} \left({x}\right)}{\mathrm{log}_{\mathrm{4}} \left({x}\right)−\mathrm{3}}\right)^{\mathrm{log}_{\mathrm{3}} \left({x}\right)} =\mathrm{2} \\…
Question Number 221397 by Nicholas666 last updated on 02/Jun/25 Commented by Nicholas666 last updated on 02/Jun/25 $$\:\:{find}\:{x} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221103 by Jgrads last updated on 24/May/25 $$\mathrm{Prove}\::\:\:\:\:\:\forall\mathrm{x}\in\mathrm{IR},\:\forall\mathrm{n}\in\mathrm{IN}^{\ast} \: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{ch}\left(\mathrm{2xt}\right)\mathrm{cos}^{\mathrm{2n}} \left(\mathrm{t}\right)\:\mathrm{dt}\:\leqslant\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}} \underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{cos}^{\mathrm{2n}} \left(\mathrm{t}\right)\:\mathrm{dt} \\ $$ Terms of…