Category: Logarithms

Question Number 14702 by tawa tawa last updated on 03/Jun/17 Answered by mrW1 last updated on 03/Jun/17 $${(\sin 6°+i\cos 6°)}^{30}$$$$={(\cos 84°+i\sin 94°)}^{30}$$$$=\cos 30\times 84°+i\sin 30\times 84°$$$$=\mathrm{cos}\:\mathrm{2529}°+\:{i}\:\mathrm{sin}\:\mathrm{2520}°\: \…

Question Number 145524 by physicstutes last updated on 05/Jul/21 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{argument}\mathrm{of}\mathrm{the}\mathrm{complex}\mathrm{numbers}\mathrm{below}$$$$\left(\mathrm{i}\right)z=1+e^{\frac{\pi }{6}i}$$$$\left(\mathrm{ii}\right)z=1-e^{\frac{\pi }{6}i}$$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\left({i}\right)\:{z}\:=\:\mathrm{1}+{e}^{{i}\frac{\pi}{\mathrm{6}}} \…

Question Number 145437 by Saiki last updated on 04/Jul/21 $$originallengthoftheironrod=175.65$$$$\mathrm{\%}increase=6\frac{1}{3}\mathrm{\%}\times 175.65$$$$=\frac{19}{3}\times \frac{1}{100}\times 175.65$$$$=\frac{19\times 175.65}{3\times 100}=\frac{3337.35}{300}=11.1245$$$$newlength=originallength+increasedlength$$$$=175.65+11.1245$$$$=186.7745cm$$$${solution}\:{by}\:{CASIO}….. \…

Question Number 145071 by imjagoll last updated on 02/Jul/21 $$\log {}_{\left(\frac{\mathrm{x}}{2}\right)}(\mathrm{x}+2)=1+\log {}_{\mathrm{x}}(4-\mathrm{x})$$$$\mathrm{x}=?$$ Answered by MJS_new last updated on 02/Jul/21 $$\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \…

Question Number 79263 by jagoll last updated on 23/Jan/20 $$4^{2\mathrm{x}-1}+\frac{1}{4}{}^2{\log }^2\left(2\mathrm{x}\right)>{}^2\log \left(\mathrm{x}\right)$$$$\{{}^2\log \left(\frac{1}{\mathrm{x}}\right)-2^{2\mathrm{x}}\}$$ Commented by john santu last…