Question Number 184989 by Ml last updated on 15/Jan/23
$$\mathrm{2}^{\mathrm{x}} =\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$$$\mathrm{solution}??? \\ $$
Answered by Frix last updated on 15/Jan/23
$$\mathrm{2}^{{x}} =\mathrm{4}{x} \\ $$$${x}=−\frac{{t}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\mathrm{e}^{−{t}} =−\frac{\mathrm{4}{t}}{\mathrm{ln}\:\mathrm{2}} \\ $$$$\mathrm{e}^{{t}} {t}=−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}} \\ $$$${t}={W}\left(−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}\right) \\ $$$${t}=\mathrm{ln}\:\frac{\mathrm{1}}{\mathrm{16}}\:\vee\:{t}\approx−.\mathrm{214811} \\ $$$$\Rightarrow\:{x}=\mathrm{4}\:\vee\:{x}\approx.\mathrm{309907} \\ $$