Question Number 65972 by gunawan last updated on 07/Aug/19 $$\mathrm{If}\:\frac{\mathrm{log}_{\mathrm{2}} \:{a}}{\mathrm{log}_{\mathrm{3}} \:{b}}={m}\:\mathrm{and}\:\frac{\mathrm{log}_{\mathrm{3}} \:{a}}{\mathrm{log}_{\mathrm{2}} \:{b}}={n} \\ $$$${a}>\mathrm{1}\:\mathrm{and}\:{b}>\mathrm{1} \\ $$$$\mathrm{then}\:\frac{{m}}{{n}}=… \\ $$$${a}.\mathrm{log}_{\mathrm{2}} \:\mathrm{3} \\ $$$${b}.\:\mathrm{log}_{\mathrm{3}} \:\mathrm{2} \\…
Question Number 131505 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{If}\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right)\:?\: \\ $$$$\mathrm{true}\:\mathrm{or}\:\mathrm{false}? \\ $$ Commented by EDWIN88 last updated…
Question Number 65970 by gunawan last updated on 07/Aug/19 $$\mathrm{log}_{\mathrm{5}} \sqrt{\mathrm{27}}×\mathrm{log}_{\mathrm{9}} \mathrm{125}+\mathrm{log}_{\mathrm{16}} \mathrm{12}=… \\ $$$${a}.\:\frac{\mathrm{61}}{\mathrm{36}} \\ $$$${b}.\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$$${c}.\:\frac{\mathrm{61}}{\mathrm{20}} \\ $$$${d}.\:\frac{\mathrm{41}}{\mathrm{12}} \\ $$$${e}.\:\frac{\mathrm{7}}{\mathrm{2}} \\ $$…
Question Number 435 by novrya last updated on 03/Jan/15 $$\int\sqrt{{cos}\:{x}}\:{dx}\:=…. \\ $$$$ \\ $$ Commented by 123456 last updated on 03/Jan/15 $$\mathrm{2E}\left(\frac{{x}}{\mathrm{2}}\mid\mathrm{2}\right)+{C} \\ $$ Commented…
Question Number 65971 by gunawan last updated on 07/Aug/19 $$\mathrm{If}\:\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{12}\:\mathrm{then}\:\mathrm{log}\left(\:^{\mathrm{3}} \sqrt{\frac{{b}}{{a}}}\right)=.. \\ $$$${a}.\:−\mathrm{2} \\ $$$${b}.\:−\mathrm{1} \\ $$$${c}.\:\mathrm{0} \\ $$$${d}.\:\mathrm{1} \\ $$$${e}.\:\mathrm{2} \\ $$…
Question Number 131507 by Chhing last updated on 05/Feb/21 $$ \\ $$$$\:\:\:\mathrm{1}/\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{2019}\right)^{\mathrm{2021}} +\left(\mathrm{2021}\right)^{\mathrm{2019}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{2020} \\ $$$$\:\:\:\mathrm{2}/\mathrm{Show}\:\mathrm{that}\:\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{7} \\ $$$$ \\ $$ Answered by JDamian…
Question Number 433 by 123456 last updated on 25/Jan/15 $$\mathrm{find}\:\mathrm{tagent}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{surface} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{3}} ={z}^{\mathrm{4}} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{28},\mathrm{8},\mathrm{6}\right) \\ $$ Answered by prakash jain last updated on…
Question Number 431 by 123456 last updated on 25/Jan/15 $$\mathrm{given} \\ $$$${x}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{3}−{x}_{{n}} } \\ $$$${x}_{\mathrm{0}} =\mathrm{2} \\ $$$$\mathrm{proof}\:\mathrm{that} \\ $$$$\mathrm{a}.\mathrm{0}<{x}_{{n}} \leqslant\mathrm{2},{n}\in\mathbb{N} \\ $$$$\mathrm{b}.{x}_{{n}} \:\mathrm{is}\:\mathrm{decreasing}…
Question Number 131497 by talminator2856791 last updated on 05/Feb/21 $$\: \\ $$$$\: \\ $$$$\:\mathrm{please}\:\mathrm{recommend}\:\mathrm{problem}\:\mathrm{and}\:\mathrm{exercise}\:\mathrm{book}\:\mathrm{for}\:\mathrm{number}\:\mathrm{theory}\: \\ $$$$\:\mathrm{where}\:\mathrm{answers}\:\mathrm{and}\:\mathrm{solutions}\:\mathrm{are}\:\mathrm{not}\:\mathrm{given}\:\mathrm{or}\:\mathrm{only} \\ $$$$\:\mathrm{given}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{book}.\:\mathrm{i}\:\mathrm{find}\:\mathrm{it}\:\mathrm{annoying}\:\mathrm{when}\:\mathrm{answers}\:\mathrm{are}\:\mathrm{always}\:\mathrm{right}\:\mathrm{next}\:\mathrm{to}\:\mathrm{the}\:\mathrm{question}. \\ $$$$\:\mathrm{a}\:\mathrm{book}\:\mathrm{that}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solutions}\:\mathrm{would}\:\mathrm{be}\:\mathrm{even}\:\mathrm{greater}. \\ $$$$\:\mathrm{the}\:\mathrm{only}\:\mathrm{such}\:\mathrm{book}\:\mathrm{i}\:\mathrm{have}\:\mathrm{found}\:\mathrm{is}\:\mathrm{250}\:\mathrm{problems}\:\mathrm{in}\:\mathrm{elementary}\:\mathrm{number}\:\mathrm{theory}. \\ $$$$\:\mathrm{thank}. \\…
Question Number 427 by 9999 last updated on 25/Jan/15 $$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{present}\:\mathrm{in} \\ $$$$\mathrm{periodic}\:\mathrm{part}\:\mathrm{for}\:\mathrm{decimal}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{11}} }? \\ $$ Commented by 123456 last updated on 02/Jan/15 $$\mathrm{10}^{{n}}…