Category: Logarithms

Question Number 107318 by bemath last updated on 10/Aug/20 $$⊚bemath⊚$$$$6^{\log {}_{(x-1)}\left(\frac{20-12x}{x-7}\right)}-36>0$$ Answered by bobhans last updated on 10/Aug/20 $$\:\:\:\:\:\:\:\:\:\circledast\mathcal{BOBHANS}\circledast \…

Question Number 107153 by bemath last updated on 09/Aug/20 $$@bemath@$$$${\left(\frac{14}{5}\right)}^{\frac{28}{\sqrt{x}}-5}={\left(\frac{5}{14}\right)}^{\frac{5}{\sqrt{x}}-160}$$ Answered by bobhans last updated on 09/Aug/20 $$\epsilon \mathrm{bobhans}\epsilon$$$$\left(\frac{\mathrm{14}}{\mathrm{5}}\right)^{\frac{\mathrm{28}}{\:\sqrt{\mathrm{x}}}−\mathrm{5}}…

Question Number 106996 by bemath last updated on 10/Aug/20 $$@bemath@$$$$\log {}_{\mid 2x-\frac{1}{2}\mid }(x+1+\frac{1}{x})⩾\log {}_{\mid 2x-\frac{1}{2}\mid }(x^2+1+\frac{1}{x^2})$$ Commented by bemath last updated on 10/Aug/20…

Question Number 172349 by Mikenice last updated on 25/Jun/22 Answered by mr W last updated on 26/Jun/22 $$\log 3\times (\log 3+\log x)=\log 4\times (\log 4+\log y)$$$$\log 4\times \log x=\log 3\times \log y$$$$letX=\log x,Y=\log y$$$${a}=\mathrm{log}\:\mathrm{3},\:{b}=\mathrm{log}\:\mathrm{4} \…

Question Number 172190 by Mikenice last updated on 23/Jun/22 Commented by mokys last updated on 23/Jun/22 $$ln\left(f\left(x\right)\right)=cos(x^2+4x+2)lnx$$$$$$$$\frac{{f}\:^{'} \left({x}\right)}{{f}\left({x}\right)}\:=\:\frac{{cos}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\right)}{{x}}\:−\:\left(\mathrm{2}{x}\:+\mathrm{4}\right){sin}\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\right){lnx}…