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Category: Algebra

Question-122854

Question Number 122854 by Study last updated on 20/Nov/20 Answered by mathmax by abdo last updated on 20/Nov/20 $$\left(−\mathrm{2}\right)^{\sqrt{\mathrm{2}}} =\mathrm{e}^{\sqrt{\mathrm{2}}\mathrm{ln}\left(−\mathrm{2}\right)} \:=\mathrm{e}^{\sqrt{\mathrm{2}}\left(\mathrm{ln}\left(−\mathrm{1}\right)+\mathrm{ln}\left(\mathrm{2}\right)\right)} \:=\mathrm{e}^{\sqrt{\mathrm{2}}\left(\mathrm{i}\pi+\mathrm{ln2}\right)} \\ $$$$=\:\mathrm{e}^{\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{2}\right)+\mathrm{i}\sqrt{\mathrm{2}}\pi} \:=\mathrm{e}^{\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{2}\right)}…

Given-x-ln-x-ln-y-5-y-ln-x-ln-y-2-then-x-y-

Question Number 122821 by bemath last updated on 19/Nov/20 $$\:{Given}\:\begin{cases}{{x}^{\mathrm{ln}\:{x}+\mathrm{ln}\:{y}} \:=\:\mathrm{5}}\\{{y}^{\mathrm{ln}\:{x}+\mathrm{ln}\:{y}} \:=\:\mathrm{2}}\end{cases} \\ $$$${then}\:\begin{cases}{{x}=?}\\{{y}=?}\end{cases} \\ $$ Answered by liberty last updated on 20/Nov/20 $$\:\begin{cases}{\mathrm{ln}\:\left({xy}\right).\mathrm{ln}\:\left({x}\right)\:=\:\mathrm{ln}\:\left(\mathrm{5}\right)\:}\\{\mathrm{ln}\:\left({xy}\right).\mathrm{ln}\:\left({y}\right)\:=\:\mathrm{ln}\:\left(\mathrm{2}\right)}\end{cases} \\…

Find-n-1-lim-x-0-1-5-25-x-2-x-5n-x-

Question Number 188343 by Shrinava last updated on 28/Feb/23 $$\mathrm{Find}:\:\Omega\:=\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}\:-\:\frac{\mathrm{5}\:-\:\sqrt{\mathrm{25}\:-\:\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}}\:\right)^{\frac{\mathrm{5}\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{x}}}} \:\right) \\ $$ Answered by SEKRET last updated on 28/Feb/23 $$\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}}…

Question-57251

Question Number 57251 by ANTARES VY last updated on 01/Apr/19 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19 $${T}_{{n}} =\frac{{n}\left({n}−\mathrm{1}\right)}{\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}+\frac{\mathrm{1}}{\left({n}−\mathrm{2}\right)!}} \\ $$$$=\frac{{n}\left({n}−\mathrm{1}\right)}{\frac{\mathrm{1}+{n}−\mathrm{1}}{\left({n}−\mathrm{1}\right)!}}\rightarrow\left({n}−\mathrm{1}\right)\left({n}−\mathrm{1}\right)! \\ $$$$\left[\underset{{n}=\mathrm{3}} {\overset{\mathrm{2019}} {\sum}}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{1}\right)!\right]+\mathrm{2}\rightarrow\boldsymbol{{S}}+\mathrm{2}…

a-8-a-4-1-a-4-a-2-1-

Question Number 57245 by ANTARES VY last updated on 01/Apr/19 $$\frac{\boldsymbol{\mathrm{a}}^{\mathrm{8}} +\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{1}}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19 $${a}^{\mathrm{8}}…