Question Number 183594 by greougoury555 last updated on 27/Dec/22 $$\:\:\:\:\:\mathrm{log}\:_{\mathrm{0}.\mathrm{5}} \:\sqrt{\mathrm{1}+{x}}\:+\:\mathrm{3log}\:_{\mathrm{0}.\mathrm{25}} \left(\mathrm{1}−{x}\right)=\:\mathrm{log}\:_{\mathrm{1}/\mathrm{16}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}\: \\ $$ Answered by hmr last updated on 27/Dec/22 $$\bullet\:\mathrm{log}\:_{\mathrm{c}}…
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Question Number 117838 by snipers237 last updated on 13/Oct/20 $$\:\:{Let}\:{be}\:{P}\:\:{the}\:{set}\:{of}\:{prime}\:{numbers}\:{and}\: \\ $$$${A}={P}\cup\left\{\mathrm{0},\mathrm{1}\right\} \\ $$$${Prove}\:{that}\:\:\:\underset{{n}\notin{A}} {\prod}\:\frac{{n}}{\:\sqrt{{n}^{\mathrm{2}} −\mathrm{1}}}\:=\frac{\mathrm{2}}{\pi}\sqrt{\mathrm{3}}\: \\ $$ Answered by mindispower last updated on 14/Oct/20…
Question Number 117826 by snipers237 last updated on 13/Oct/20 $$\:\:{Prove}\:{that}\:{the}\:{Euler}\:{Constant}\:{is}\:{qlso}\:{equal}\:{to} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\:\Gamma\left({x}\right)−\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)} \\ $$ Answered by mnjuly1970 last updated on 14/Oct/20 $${solution}:: \\ $$$$\:{lim}_{{x}\rightarrow−\mathrm{1}}…
Question Number 117816 by snipers237 last updated on 13/Oct/20 $$\:\:{find}\:{out}\:\:\:{for}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\Gamma\left(\mathrm{1}+\frac{{k}}{{n}}\right) \\ $$$$ \\ $$ Answered by mnjuly1970 last updated on 14/Oct/20…
Question Number 52030 by Water last updated on 02/Jan/19 $${given}\:{that}\:{log}\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{log}\mathrm{3}=\mathrm{0}.\mathrm{477}\:{log}\mathrm{5}=\mathrm{0}.\mathrm{699} \\ $$$${find}\:{the}\:{values}\:{of}\:{log}\sqrt{\left(\mathrm{0}.\mathrm{2}\right)} \\ $$$$ \\ $$ Answered by afachri last updated on 02/Jan/19 $$\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)^{\mathrm{0}.\mathrm{5}} =\:\mathrm{0}.\mathrm{5}\:\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)…
Question Number 182904 by mathlove last updated on 16/Dec/22 Answered by balliu last updated on 16/Dec/22 $$\sqrt{\mathrm{3}}\left({cosx}+{sinx}\right)−\left({cosx}−{sinx}\right)=\sqrt{\mathrm{2}} \\ $$$$\left(\sqrt{\mathrm{3}}−\mathrm{1}\right){cosx}+\left(\sqrt{\mathrm{3}}+\mathrm{1}\right){sinx}=\sqrt{\mathrm{2}} \\ $$$$ \\ $$ Terms of…
Question Number 182737 by cortano1 last updated on 13/Dec/22 Answered by dre23 last updated on 14/Dec/22 $${d}=\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}−\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)}=−\mathrm{15}\frac{{ln}\left({z}\right)}{{ln}\left({x}\right)}−\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}=\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)}−\mathrm{1}={d} \\ $$$${d}+\mathrm{1}=\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)} \\ $$$$\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}=\mathrm{2}{d}+\mathrm{1} \\ $$$$−\mathrm{15}\frac{{ln}\left({z}\right)}{{ln}\left({x}\right).}=\mathrm{3}{d}+\mathrm{1} \\ $$$$\frac{{ln}\left({x}\right)}{{ln}\left({z}\right)}=−\frac{\mathrm{15}}{\left(\mathrm{1}+\mathrm{3}{d}\right)}=\left({d}+\mathrm{1}\right)\left(\mathrm{2}{d}+\mathrm{1}\right)…
Question Number 182632 by cortano1 last updated on 12/Dec/22 $$\:\:\mathrm{If}\:\mathrm{log}\:_{\mathrm{11}} \left(\mathrm{3p}\right)=\mathrm{log}\:_{\mathrm{13}} \left(\mathrm{q}+\mathrm{6p}\right)\:=\:\mathrm{log}\:_{\mathrm{143}} \left(\mathrm{q}^{\mathrm{2}} \right) \\ $$$$\:\mathrm{find}\:\frac{\mathrm{p}}{\mathrm{q}}. \\ $$ Answered by manxsol last updated on 12/Dec/22…
Question Number 116976 by bobhans last updated on 08/Oct/20 $$\mathrm{use}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{P}=\mathrm{Ie}^{\mathrm{kt}} \:,\mathrm{where}\:\mathrm{P}\:\mathrm{is}\:\mathrm{resulting} \\ $$$$\mathrm{population}\:,\mathrm{I}\:\mathrm{is}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{population}\:\mathrm{and}\:\mathrm{t}\:\mathrm{is} \\ $$$$\mathrm{measured}\:\mathrm{in}\:\mathrm{hours}.\:\mathrm{A}\:\mathrm{bacterial}\:\mathrm{culture} \\ $$$$\mathrm{has}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{population}\:\mathrm{of}\:\mathrm{10},\mathrm{000}.\:\mathrm{If} \\ $$$$\mathrm{its}\:\mathrm{declines}\:\mathrm{to}\:\mathrm{5000}\:\mathrm{in}\:\mathrm{6}\:\mathrm{hours}\:,\:\mathrm{what}\: \\ $$$$\mathrm{will}\:\mathrm{it}\:\mathrm{be}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{8}\:\mathrm{hours}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1985}\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{3969}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2500}\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{4353} \\ $$…