Category: Logarithms

Question Number 12489 by Joel577 last updated on 23/Apr/17 $${\log }_{2}x+{\log }_{1/x}\frac{1}{2}⩾0$$$$x=?$$ Answered by mrW1 last updated on 23/Apr/17 $$\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{2}}+\frac{\mathrm{ln}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{ln}\:\left(\frac{\mathrm{1}}{{x}}\right)}\geqslant\mathrm{0} \…

Question Number 12284 by tawa last updated on 17/Apr/17 Answered by mrW1 last updated on 18/Apr/17 $$lett=\frac{1}{2x}$$$${\log }_5(5^{\frac{1}{x}}+125)={\log }_{5}6+1+\frac{1}{2x}\Rightarrow$$$$\mathrm{log}_{\mathrm{5}} \:\left(\mathrm{5}^{\mathrm{2}{t}}…

Question Number 142755 by ERA last updated on 05/Jun/21 $${\log }_3{\mathrm{x}}^3+{\log }_2{\mathrm{x}}^2=\frac{2\lg 6}{\lg 2}+1\mathrm{find}\mathrm{x}$$ Commented by iloveisrael last updated on 05/Jun/21 $${what}\:{different}\:\mathrm{log}\:\:{and}\:\mathrm{lg}\:? \…

Question Number 11383 by tawa last updated on 22/Mar/17 $$\mathrm{There}\mathrm{are}\mathrm{six}\mathrm{trains}\mathrm{travelling}\mathrm{between}\mathrm{Abuja}\mathrm{and}\mathrm{Lagos}\mathrm{and}\mathrm{back}.$$$$\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}\mathrm{a}\mathrm{man}\mathrm{travel}\mathrm{from}\mathrm{abuja}\mathrm{to}\mathrm{Lagos}\mathrm{by}\mathrm{one}\mathrm{train}\mathrm{and}$$$$\mathrm{return}\mathrm{by}\mathrm{a}\mathrm{different}\mathrm{train}$$ Answered by sandy_suhendra last updated on 23/Mar/17 $$\mathrm{Abuja}\:\mathrm{to}\:\mathrm{Lagos}\:=\:\mathrm{6}\:\mathrm{trains} \…

Question Number 141365 by bemath last updated on 18/May/21 $$\log {}_{\frac{9}{4}}\left(\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{\dots }}}}\right)=?$$ Answered by EDWIN88 last updated on 18/May/21 $$\mathrm{let}\mathcal{E}=\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{\dots }}}}$$$$\Rightarrow \mathcal{E}=\frac{1}{2\sqrt{3}}\sqrt{6-\mathcal{E}}$$$$\Rightarrow\:\mathcal{E}^{\mathrm{2}}…