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 34792 by mondodotto@gmail.com last updated on 11/May/18

solve for x 4x=2^x

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{4}\boldsymbol{{x}}=\mathrm{2}^{\boldsymbol{{x}}} \\ $$

Answered by Joel579 last updated on 11/May/18

Commented by Joel579 last updated on 11/May/18

Real solution x = 0.3099 x = 4

$$\mathrm{Real}\:\mathrm{solution} \\ $$$${x}\:=\:\mathrm{0}.\mathrm{3099} \\ $$$${x}\:=\:\mathrm{4} \\ $$

Answered by mr W last updated on 13/Jan/19

4x=e^(xln 2) xe^(−xln 2) =(1/4) (−xln 2)e^(−xln 2) =−((ln 2)/4) ⇒−x ln 2=W(−((ln 2)/4)) ⇒x=−((W(−((ln 2)/4)))/(ln 2))= { ((−((−0.2148)/(ln 2))=0.3099)),((−((−2.7726)/(ln 2))=4)) :}

$$\mathrm{4}{x}={e}^{{x}\mathrm{ln}\:\mathrm{2}} \\ $$$${xe}^{−{x}\mathrm{ln}\:\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left(−{x}\mathrm{ln}\:\mathrm{2}\right){e}^{−{x}\mathrm{ln}\:\mathrm{2}} =−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}} \\ $$$$\Rightarrow−{x}\:\mathrm{ln}\:\mathrm{2}={W}\left(−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}\right) \\ $$$$\Rightarrow{x}=−\frac{{W}\left(−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}\right)}{\mathrm{ln}\:\mathrm{2}}=\begin{cases}{−\frac{−\mathrm{0}.\mathrm{2148}}{\mathrm{ln}\:\mathrm{2}}=\mathrm{0}.\mathrm{3099}}\\{−\frac{−\mathrm{2}.\mathrm{7726}}{\mathrm{ln}\:\mathrm{2}}=\mathrm{4}}\end{cases} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com