Menu Close

2-x-6-2-x-10-2-x-2-4-2-x-1-2-x-2-Find-x-




Question Number 207218 by hardmath last updated on 09/May/24
2^x   +  ((6 ∙ 2^x  − 10)/(2^x  − 2))  =  4 ∙ 2^x   +  (1/(2^x  − 2))  Find:   x = ?
$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:+\:\:\frac{\mathrm{6}\:\centerdot\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{10}}{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}}\:\:=\:\:\mathrm{4}\:\centerdot\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$
Answered by Frix last updated on 10/May/24
Transform to  (2^x )^2 −4×2^x +((11)/3)=0  2^x =2±((√3)/3)  x=((ln (6±(√3)) −ln 3)/(ln 2))
$$\mathrm{Transform}\:\mathrm{to} \\ $$$$\left(\mathrm{2}^{{x}} \right)^{\mathrm{2}} −\mathrm{4}×\mathrm{2}^{{x}} +\frac{\mathrm{11}}{\mathrm{3}}=\mathrm{0} \\ $$$$\mathrm{2}^{{x}} =\mathrm{2}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$${x}=\frac{\mathrm{ln}\:\left(\mathrm{6}\pm\sqrt{\mathrm{3}}\right)\:−\mathrm{ln}\:\mathrm{3}}{\mathrm{ln}\:\mathrm{2}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *