Question Number 56356 by Tawa1 last updated on 15/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{F}\left(\mathrm{x}\right)\:=\:\:\mathrm{log}_{\mathrm{e}} \mathrm{x}\:\:−\:\:\mathrm{x}\:\:\:\mathrm{for}\:\:\:\mathrm{x}\:>\:\mathrm{0}. \\ $$$$\:\:\mathrm{Hence}\:\mathrm{show}\:\mathrm{that}:\:\:\:\mathrm{log}_{\mathrm{e}} \mathrm{x}\:\:\leqslant\:\:\mathrm{x}\:−\:\mathrm{1}.\:\:\mathrm{For}\:\mathrm{all}\:\:\:\mathrm{x}\:>\:\mathrm{0} \\ $$ Commented by Tawa1 last updated on 15/Mar/19 Answered by…
Question Number 121889 by oustmuchiya@gmail.com last updated on 12/Nov/20 Answered by Dwaipayan Shikari last updated on 12/Nov/20 $$\left(\mathrm{1}+{ax}\right)^{{b}} =\mathrm{1}+\mathrm{48}{x}+\mathrm{1008}{x}^{\mathrm{2}} +… \\ $$$${ab}=\mathrm{48} \\ $$$${a}^{\mathrm{2}} \frac{{b}\left({b}−\mathrm{1}\right)}{\mathrm{2}}=\mathrm{1008}…
Question Number 56335 by Tawa1 last updated on 14/Mar/19 $$\mathrm{If}\:\:\:\:\:\:\mathrm{b}^{\mathrm{x}} \:\:=\:\:\left(\frac{\mathrm{b}}{\mathrm{k}}\right)^{\mathrm{y}} \:\:=\:\:\mathrm{k}^{\mathrm{m}} \:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{b}\:\neq\:\mathrm{1} \\ $$$$\mathrm{show}\:\mathrm{that}:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\frac{\mathrm{1}}{\mathrm{y}}\:=\:\frac{\mathrm{1}}{\mathrm{m}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 14/Mar/19 $${b}^{{x}}…
Question Number 187388 by ajfour last updated on 16/Feb/23 $${p}^{\mathrm{3}} +{q}^{\mathrm{3}} ={c}\:\:\:,\:\:{pq}=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\forall\:\:\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${Find}\:{p}+{q}. \\ $$ Answered by anurup last updated on 17/Feb/23 $$ \\…
Question Number 56316 by Sr@2004 last updated on 14/Mar/19 Commented by Sr@2004 last updated on 14/Mar/19 $$\mathrm{1}\:{er}\mathrm{4}\:{no}.{ta}\:{please}\:{solve}\:{kore}\:{din} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 187381 by a.lgnaoui last updated on 16/Feb/23 $$\mathrm{3}^{{x}} =\mathrm{5}^{{y}} =\mathrm{225} \\ $$$${Determiner}:\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:? \\ $$ Answered by horsebrand11 last updated on 16/Feb/23 $$\:\begin{cases}{{x}=\mathrm{log}\:_{\mathrm{3}} \mathrm{225}}\\{{y}=\mathrm{log}\:_{\mathrm{5}}…
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Question Number 187373 by Shrinava last updated on 16/Feb/23 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 187357 by cortano12 last updated on 16/Feb/23 Answered by Humble last updated on 16/Feb/23 $$\mathrm{3}\sqrt{\mathrm{5}}\sqrt{\mathrm{2}{x}+\mathrm{3}}\:+\mathrm{2}\sqrt{\mathrm{5}}\sqrt{\mathrm{3}{x}+\mathrm{2}}\:=\:\sqrt{\mathrm{3}{x}+\mathrm{2}}\sqrt{\mathrm{2}{x}+\mathrm{3}} \\ $$$$ \\ $$$$\mathrm{21600}{x}^{\mathrm{2}} +\mathrm{46800}{x}+\mathrm{21600}=\mathrm{36}{x}^{\mathrm{4}} −\mathrm{1644}{x}^{\mathrm{3}} +\mathrm{16741}{x}^{\mathrm{2}} +\mathrm{46306}{x}+\mathrm{28561}…
Question Number 56264 by ajfour last updated on 13/Mar/19 $$\left({x}_{{C}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}−{x}_{{C}} \right)^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \\ $$$$\:\left({x}_{{A}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}+{x}_{{A}} \right)^{\mathrm{2}} =\:{c}^{\mathrm{2}} \\ $$$$\:\:\left({x}_{{C}} −{x}_{{A}} \right)^{\mathrm{2}} \:=\:{b}^{\mathrm{2}}…