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…
Question Number 218279 by Tawa11 last updated on 04/Apr/25 $$\mathrm{Evaluate}: \\ $$$$\:\:\:\:\:\frac{\mathrm{4}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} } \\ $$$$\mathrm{Show}\:\mathrm{workings}\:\mathrm{please}. \\ $$ Answered by Frix last updated…
Question Number 217691 by PaulDirac last updated on 18/Mar/25 Answered by mr W last updated on 19/Mar/25 $${let}\:{a}=\mathrm{9}^{\mathrm{9}^{\mathrm{9}} } \\ $$$${I}=\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\:\left({ax}\right){dx} \\ $$$$\:\:=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}}…
Question Number 215951 by alcohol last updated on 22/Jan/25 $${E}_{{n}} \:=\:\mathrm{3}^{{E}_{{n}−\mathrm{1}} } ,\:{n}\geqslant\mathrm{2} \\ $$$${find}\:{the}\:{unit}\:{digit}\:{of}\:{E}_{\mathrm{1000}} \\ $$ Answered by A5T last updated on 22/Jan/25 $$\mathrm{3}^{\mathrm{3}^{\mathrm{3}^{\mathrm{x}}…