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Category: Logarithms

Given-that-1-log-3-x-log-27-y-express-y-in-terms-of-x-

Question Number 53675 by pieroo last updated on 24/Jan/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{1}+\mathrm{log}_{\mathrm{3}} \mathrm{x}\:=\mathrm{log}_{\mathrm{27}} \mathrm{y},\:\mathrm{express}\:\mathrm{y} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by kaivan.ahmadi last updated on 24/Jan/19 $$\mathrm{log}_{\mathrm{3}} \mathrm{3}+\mathrm{log}_{\mathrm{3}}…

log-0-5-1-x-3log-0-25-1-x-log-1-16-1-x-2-2-2-

Question Number 183594 by greougoury555 last updated on 27/Dec/22 $$\:\:\:\:\:\mathrm{log}\:_{\mathrm{0}.\mathrm{5}} \:\sqrt{\mathrm{1}+{x}}\:+\:\mathrm{3log}\:_{\mathrm{0}.\mathrm{25}} \left(\mathrm{1}−{x}\right)=\:\mathrm{log}\:_{\mathrm{1}/\mathrm{16}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}\: \\ $$ Answered by hmr last updated on 27/Dec/22 $$\bullet\:\mathrm{log}\:_{\mathrm{c}}…

Let-be-P-the-set-of-prime-numbers-and-A-P-0-1-Prove-that-n-A-n-n-2-1-2-pi-3-

Question Number 117838 by snipers237 last updated on 13/Oct/20 $$\:\:{Let}\:{be}\:{P}\:\:{the}\:{set}\:{of}\:{prime}\:{numbers}\:{and}\: \\ $$$${A}={P}\cup\left\{\mathrm{0},\mathrm{1}\right\} \\ $$$${Prove}\:{that}\:\:\:\underset{{n}\notin{A}} {\prod}\:\frac{{n}}{\:\sqrt{{n}^{\mathrm{2}} −\mathrm{1}}}\:=\frac{\mathrm{2}}{\pi}\sqrt{\mathrm{3}}\: \\ $$ Answered by mindispower last updated on 14/Oct/20…

Prove-that-the-Euler-Constant-is-qlso-equal-to-lim-x-1-x-1-x-x-1-

Question Number 117826 by snipers237 last updated on 13/Oct/20 $$\:\:{Prove}\:{that}\:{the}\:{Euler}\:{Constant}\:{is}\:{qlso}\:{equal}\:{to} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\:\Gamma\left({x}\right)−\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)} \\ $$ Answered by mnjuly1970 last updated on 14/Oct/20 $${solution}:: \\ $$$$\:{lim}_{{x}\rightarrow−\mathrm{1}}…

given-that-log2-0-3010-log3-0-477-log5-0-699-find-the-values-of-log-0-2-

Question Number 52030 by Water last updated on 02/Jan/19 $${given}\:{that}\:{log}\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{log}\mathrm{3}=\mathrm{0}.\mathrm{477}\:{log}\mathrm{5}=\mathrm{0}.\mathrm{699} \\ $$$${find}\:{the}\:{values}\:{of}\:{log}\sqrt{\left(\mathrm{0}.\mathrm{2}\right)} \\ $$$$ \\ $$ Answered by afachri last updated on 02/Jan/19 $$\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)^{\mathrm{0}.\mathrm{5}} =\:\mathrm{0}.\mathrm{5}\:\mathrm{log}\:\left(\frac{\mathrm{2}}{\mathrm{10}}\right)…

Question-182904

Question Number 182904 by mathlove last updated on 16/Dec/22 Answered by balliu last updated on 16/Dec/22 $$\sqrt{\mathrm{3}}\left({cosx}+{sinx}\right)−\left({cosx}−{sinx}\right)=\sqrt{\mathrm{2}} \\ $$$$\left(\sqrt{\mathrm{3}}−\mathrm{1}\right){cosx}+\left(\sqrt{\mathrm{3}}+\mathrm{1}\right){sinx}=\sqrt{\mathrm{2}} \\ $$$$ \\ $$ Terms of…

Question-182737

Question Number 182737 by cortano1 last updated on 13/Dec/22 Answered by dre23 last updated on 14/Dec/22 $${d}=\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}−\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)}=−\mathrm{15}\frac{{ln}\left({z}\right)}{{ln}\left({x}\right)}−\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}=\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)}−\mathrm{1}={d} \\ $$$${d}+\mathrm{1}=\frac{{ln}\left({x}\right)}{{ln}\left({y}\right)} \\ $$$$\frac{{ln}\left({y}\right)}{{ln}\left({z}\right)}=\mathrm{2}{d}+\mathrm{1} \\ $$$$−\mathrm{15}\frac{{ln}\left({z}\right)}{{ln}\left({x}\right).}=\mathrm{3}{d}+\mathrm{1} \\ $$$$\frac{{ln}\left({x}\right)}{{ln}\left({z}\right)}=−\frac{\mathrm{15}}{\left(\mathrm{1}+\mathrm{3}{d}\right)}=\left({d}+\mathrm{1}\right)\left(\mathrm{2}{d}+\mathrm{1}\right)…