Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 11714 by Nayon last updated on 30/Mar/17

$$SolvetheCrazyequation...$$$$x{\left(lnx\right)}^2+xlnx-1=0$$

Commented by mrW1 last updated on 30/Mar/17

$$\ln x=\frac{\sqrt{1+\frac{4}{x}}-1}{2}$$$$I{don}^{\prime }tthinkthereisananalytical$$$$solution.$$

Commented by FilupS last updated on 31/Mar/17

$$x{\ln }^{2}x+x\ln x=1$$$$e^{\ln \left(x^{x\ln x}\right)+x\ln \left(x\right)}=e$$$$x\ln x=u$$$$x=e^{W\left(u\right)}\mathrm{product}\log \mathrm{function}$$$$e^{u\ln \left(e^{W\left(u\right)}\right)+u}=e$$$$e^{uW\left(u\right)+u}=e$$$$e^{u(W\left(u\right)+1)}=e$$$$\therefore u(W\left(u\right)+1)=1$$$$W\left(u\right)=\frac{1}{u}-1$$$$$$$$A\mathrm{s}\mathrm{said}\mathrm{above},\mathrm{I}\mathrm{am}\mathrm{unsure}\mathrm{an}\mathrm{analytical}$$$$\mathrm{solution}\mathrm{exists}$$$$$$$$Pleasecorrectanymistakes$$

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 07/Apr/17

Terms of Service

Privacy Policy

Contact: info@tinkutara.com