Question Number 4413 by alib last updated on 22/Jan/16 $$\boldsymbol{\mathrm{C}}\mathrm{alculate}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{2}^{\boldsymbol{{x}}} +\mathrm{2}^{−\boldsymbol{{x}}} , \\ $$$$\mathrm{if}\:\mathrm{4}^{\boldsymbol{{x}}} +\mathrm{4}^{−\boldsymbol{{x}}} =\mathrm{23} \\ $$$$ \\ $$ Answered by prakash jain last…
Question Number 4399 by alib last updated on 22/Jan/16 $${Solve}\:{for}\:{x} \\ $$$$ \\ $$$${x}^{\mathrm{2}\:{log}\:_{\mathrm{2}} \:{x}} =\mathrm{8} \\ $$ Commented by Rasheed Soomro last updated on…
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Question Number 69018 by Maclaurin Stickker last updated on 17/Sep/19 Commented by Prithwish sen last updated on 18/Sep/19 $$\mathrm{It}\:\mathrm{is}\:\mathrm{only}\:\mathrm{possible}\:\mathrm{when} \\ $$$$\mathrm{4}\boldsymbol{\mathrm{a}}+\mathrm{5}\boldsymbol{\mathrm{b}}+\mathrm{1}=\mathrm{8}\boldsymbol{\mathrm{ab}}+\mathrm{1} \\ $$$$\Rightarrow\mathrm{4}\boldsymbol{\mathrm{a}}+\mathrm{5}\boldsymbol{\mathrm{b}}=\mathrm{8}\boldsymbol{\mathrm{ab}}…………\left(\boldsymbol{\mathrm{i}}\right) \\ $$$$\boldsymbol{\mathrm{and}}…
Question Number 3239 by Rasheed Soomro last updated on 08/Dec/15 $$\mathcal{I}\:{don}'{t}\:{know}\:{the}\:{value}\:{of}\:\:{Log}\left(−\mathrm{1}\right)\:{but}\:{I}\:{calculate} \\ $$$${it}\:{in}\:{the}\:{following}\:{way}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$$\:\:\:\:\:\Rightarrow\:\:{Log}\left(−\mathrm{1}\right)^{\mathrm{2}} ={Log}\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\Rightarrow\:\:\mathrm{2}×{Log}\left(−\mathrm{1}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\Rightarrow\:{Log}\left(−\mathrm{1}\right)=\frac{\mathrm{0}}{\mathrm{2}}=\mathrm{0} \\ $$$${Am}\:\mathcal{I}\:{correct}?\:\mathcal{I}{f}\:{no},{why}?…
Question Number 68712 by Rio Michael last updated on 15/Sep/19 $${given}\:{that}\:{x}\:{and}\:{y}\:{are}\:{two}\:{numbers}\:{other}\:{one}.\: \\ $$$${given}\:{that}\:\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$${and}\:\:{a}^{{x}} \:=\:{b}^{{y}} \:=\:\left({ab}\right)^{{xy}} \:\:{show}\:{that}\:\:{x}\:+\:{y}\:=\mathrm{0} \\ $$ Commented by Prithwish sen last…
Question Number 3160 by prakash jain last updated on 06/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:{e}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}!}\:\:\mathrm{is}\:\mathrm{irrational}. \\ $$ Answered by Yozzi last updated on 06/Dec/15 $${Fourier}'{s}\:{Proof} \\ $$$${Suppose}\:{for}\:{contradiction}\:{that}…
Question Number 68616 by Rio Michael last updated on 14/Sep/19 $${given}\:{that}\:{a},{b}\:{and}\:{c}\:{are}\:{positive}\:{numbers}\:{other}\:{than}\:\mathrm{1} \\ $$$$,\:{show}\:{that}\:\:{log}_{{b}} {a}\:×\:{log}_{{c}} {b}\:×\:{log}_{{a}} {c}\:=\:\mathrm{1} \\ $$$${hence},\:{evaluate}\:\:\:{log}_{\mathrm{10}} \mathrm{25}\:×\:{log}_{\mathrm{2}} \mathrm{10}\:×\:{log}_{\mathrm{5}} \mathrm{4} \\ $$ Answered by…
Question Number 68618 by Rio Michael last updated on 14/Sep/19 $${solve}\:{for}\:{x}\:{the}\:{following}\:{equations} \\ $$$$\left.{a}\right)\:{log}\:{x}^{\mathrm{3}} \:−\:\mathrm{2}{log}\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{log}\:{x}\:\:+\:\mathrm{2}{log}\:\sqrt{{x}}\:=\:\mathrm{3} \\ $$$$\left.{b}\right)\:{log}_{{x}} \mathrm{24}\:−\mathrm{3}{log}_{{x}} \mathrm{4}\:\:+\:\mathrm{2}{log}_{{x}} \mathrm{3}\:=−\mathrm{3} \\ $$ Answered by Rasheed.Sindhi…
Question Number 134116 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{8}\right) \\ $$$$\:\Leftrightarrow\:\frac{\mathrm{x}+\mathrm{3}}{\mathrm{x}}\:=\:\mathrm{8}\:,\:\mathrm{3}\:=\:\mathrm{7x}\:,\:\mathrm{x}\:=\:\frac{\mathrm{3}}{\mathrm{7}} \\ $$ Terms…