Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 103503 by 175mohamed last updated on 15/Jul/20

$$$$$$Solve:$$$$3^x=4x$$

Answered by Dwaipayan Shikari last updated on 15/Jul/20

$$e^{xlog3}=4x$$$$e^{-xlog3}=\frac{1}{4x}$$$$-xlog3e^{-xlog3}=-\frac{log3}{4}$$$$-xlog3=W_0(-\frac{log3}{4})$$$$x=-\frac{W_0(-\frac{log3}{4})}{log3}=0.379...$$$$orx=1.794273...$$

Commented by mr W last updated on 15/Jul/20

$$W(-\frac{\ln 3}{4})hastwovalues.$$

Answered by OlafThorendsen last updated on 15/Jul/20

$$f\left(x\right)=x\ln 3-\ln x-2\ln 2,x>0$$$$f^{\prime }\left(x\right)=\ln 3-\frac{1}{x}$$$$f^{\prime }\left(x\right)=0\iff x=\frac{1}{\ln 3}$$$$f\left(\frac{1}{\ln 3}\right)=1+\ln \left(\ln 3\right)-2\ln 2$$$$f\left(\frac{1}{\ln 3}\right)\approx -0,29<0$$$$\underset{x\to 0^{-}}{\lim }f\left(x\right)=+\mathrm{\infty }$$$$\underset{x\to +\mathrm{\infty }}{\lim }f\left(x\right)=+\mathrm{\infty }$$$$\Rightarrow \mathrm{two}\mathrm{solutions}\mathrm{for}f\left(x\right)=0$$$$x\approx 0,379\mathrm{or}x\approx 1,794$$$$\mathrm{and}f\left(x\right)=0\iff 3^x=4x$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com