Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 66478 by hmamarques1994@gmail.com last updated on 15/Aug/19

$$$$$$\underset{\mathit{x}\to 2}{\mathit{l}\mathit{i}\mathit{m}}\left[\frac{{\mathit{l}\mathit{o}\mathit{g}}_{\mathit{x}}\left(2\right)-1}{{\mathit{l}\mathit{o}\mathit{g}}_2\left(\frac{1}{\mathit{x}}\right)+1}\right]=?$$$$$$

Commented by gunawan last updated on 16/Aug/19

$$\underset{x\to 2}{\lim }\frac{{\log }_{x}2-{\log }_{x}x}{{\log }_2\left(\frac{1}{x}\right)+{\log }_{2}2}$$$$=\underset{x\to 2}{\lim }\frac{{\log }_x\left(\frac{2}{x}\right)}{{\log }_2\left(\frac{1}{2x}\right)}=\frac{{\log }_2\left(\frac{2}{2}\right)}{{\log }_2\left(\frac{1}{4}\right)}=\frac{{\log }_{2}1}{-2\times {\log }_2}=0$$

Commented by Rasheed.Sindhi last updated on 16/Aug/19

$${\log }_2\left(\frac{1}{x}\right)+{\log }_{2}2={\log }_2\left(\frac{1}{\mathrm{x}}\times 2\right)={\log }_2\left(\frac{2}{\mathrm{x}}\right)$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com