Category: Logarithms

Question Number 193183 by York12 last updated on 06/Jun/23 $$$$$$Thereexistsauniquepositiveintegerafor$$$$whichThesumu=\underset{n=1}{\sum ^{2023}}\lfloor \frac{n^2-na}{5}\rfloor isaninteger$$$$strictlybetween-1000\mathrm{\&}1000finda+u.$$ Answered by York12 last…

Question Number 65333 by aliesam last updated on 28/Jul/19 Commented by Prithwish sen last updated on 28/Jul/19 $${\log }_{\mathrm{y}}\mathrm{x}=\mathrm{v}\Rightarrow \frac{{\mathrm{v}}^2+1}{\mathrm{v}}=\frac{17}{4}\Rightarrow {4\mathrm{v}}^2-17\mathrm{v}+4=0$$$$\mathrm{4v}^{\mathrm{2}} −\mathrm{16v}−\mathrm{v}+\mathrm{4}=\mathrm{0}\Rightarrow\mathrm{4v}\left(\mathrm{v}−\mathrm{4}\right)−\mathrm{1}\left(\mathrm{v}−\mathrm{4}\right)=\mathrm{0} \…

Question Number 130553 by Study last updated on 26/Jan/21 $$log(x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\dots .)=?$$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${log}\left(−{log}\left(\mathrm{1}−{x}\right)\right)={log}\left({log}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)\right) \…

Question Number 130244 by Adel last updated on 23/Jan/21 Commented by mr W last updated on 23/Jan/21 $${it}^{\prime }snottounderstand:thisquestion$$$$isaskedalreadyfourtimes,three$$$$timesalonefromyou!{what}^{\prime }sthe$$$${sense}?\:{if}\:{you}\:{don}'{t}\:{understand}\:{the} \…

Question Number 129088 by Gulnoza last updated on 12/Jan/21 Answered by MJS_new last updated on 12/Jan/21 $$4^{{2\log }_{4}x}={\left(4^{{\log }_{4}x}\right)}^2=x^2=25$$$$\Rightarrow\:{x}=\pm\mathrm{5}…