Question Number 187295 by Michaelfaraday last updated on 15/Feb/23 $${solve}: \\ $$$$\left(\sqrt{\left.\mathrm{4}+\sqrt{\mathrm{4}}\right)\:^{{x}} }\:+\left[\sqrt{\mathrm{4}−\sqrt{\left.\mathrm{4}\right]^{{x}} }}\:=\mathrm{4}^{{x}} \right.\right. \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{not}\:\mathrm{clear}…
Question Number 187294 by Michaelfaraday last updated on 15/Feb/23 $${solve}: \\ $$$$−\mathrm{1}−\left[{x}^{{x}} −\mathrm{5}{x}+\mathrm{6}\right]^{{x}} =\mathrm{1} \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\left[{t}\right]=\lfloor{t}\rfloor\:\mathrm{or}\:…? \\…
Question Number 187288 by mathlove last updated on 15/Feb/23 $${logx}+{x}!=\mathrm{2} \\ $$$${x}=? \\ $$ Answered by Frix last updated on 15/Feb/23 $${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{solution} \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{mean} \\…
Question Number 121754 by bemath last updated on 11/Nov/20 Answered by liberty last updated on 11/Nov/20 $$\mathrm{let}\:\mathrm{y}\:=\:\left(\mathrm{2020}!\right)^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{ln}\:\mathrm{y}\:=\:\mathrm{2}\left(\mathrm{ln}\:\mathrm{2020}+\mathrm{ln}\:\mathrm{2019}+\mathrm{ln}\:\mathrm{2018}+…+\mathrm{ln}\:\mathrm{1}\right) \\ $$$$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{2020}^{\mathrm{2020}} \\ $$$$\Rightarrow\mathrm{ln}\:\mathrm{x}\:=\:\mathrm{2020}\:\mathrm{ln}\:\left(\mathrm{2020}\right)\: \\ $$$$…
Question Number 56192 by 121194 last updated on 11/Mar/19 $$\mathrm{find}\:{z}_{\mathrm{1}} ,{z}_{\mathrm{2}} \in\mathbb{C} \\ $$$$\frac{\mathrm{1}}{{z}_{\mathrm{1}} +{z}_{\mathrm{2}} }=\frac{\mathrm{1}}{{z}_{\mathrm{1}} }+\frac{\mathrm{1}}{{z}_{\mathrm{2}} } \\ $$ Answered by MJS last updated…
Question Number 121720 by Jamshidbek2311 last updated on 11/Nov/20 $${Does}\:{this}\:{example}\:{work}\:{that}\:{way}. \\ $$$${f}\left({x}\right)={x}^{{x}} \:\:\:{f}'\left({x}\right)={x}^{{x}} \centerdot\left({lnx}+\mathrm{1}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 11/Nov/20 $${f}\left({x}\right)={x}^{{x}}…
Question Number 56183 by 121194 last updated on 11/Mar/19 $$\mathrm{find}\:\mathrm{all}\:{a},{b}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}+{bi}}=\frac{\mathrm{1}}{{a}}+\frac{{i}}{{b}} \\ $$ Answered by kaivan.ahmadi last updated on 11/Mar/19 $$\frac{\mathrm{1}}{{a}+{bi}}=\frac{{b}+{ai}}{{ab}}\Rightarrow{ab}+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right){i}−{ab}={ab}\Rightarrow \\…
Question Number 187255 by Spillover last updated on 15/Feb/23 $${Find}\:{the}\:{directional}\:{derivatives}\:{of}\:{the} \\ $$$${function}\: \\ $$$${f}\left({x},\mathrm{y},\mathrm{z}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:{at}\:{the}\:{point}\:{p}\left(\mathrm{2},\mathrm{1},\mathrm{3}\right) \\ $$ Answered by MikeH last updated on…
Question Number 187254 by mnjuly1970 last updated on 15/Feb/23 Answered by MJS_new last updated on 15/Feb/23 $${c}={a}+{b}\:\Rightarrow\:{E}=\frac{\mathrm{2}\left({a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \right)^{\mathrm{2}} }{{ab}}>\mathrm{0} \\ $$ Terms of Service…
Question Number 187248 by MWSuSon last updated on 15/Feb/23 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{whose} \\ $$$$\mathrm{base}\:\mathrm{ten}\:\mathrm{digits}\:\mathrm{sums}\:\mathrm{up}\:\mathrm{to}\:\mathrm{10} \\ $$ Commented by Frix last updated on 15/Feb/23 $$\mathrm{Same}\:\mathrm{as}\:\mathbb{N} \\ $$ Terms…