Question Number 100879 by Tony6400 last updated on 29/Jun/20

Solve the equation 2^x +8x=4

Commented bybemath last updated on 29/Jun/20

approximation x = 0.342

Answered by 1549442205 last updated on 07/Jul/20

⇔2^(x−2) +2x−1=0.Putting f(x)=2^(x−2) +2x−1 f ′(x)=2^(x−2) ln2+2>0∀x∈(−∞;+∞) f(x)=0⇔x=0.3416043768 Since f(x) is increasing ,the given equation has only root x=0.3416043768

Answered by mr W last updated on 29/Jun/20

2^x =8((1/2)−x) e^(xln 2) =8((1/2)−x) (((√2) ln 2)/8) =[((1/2)−x)ln 2]e^(((1/2)−x)ln 2) ((1/2)−x)ln 2=W((((√2) ln 2)/8)) ⇒x=(1/2)−(1/(ln 2))W((((√2) ln 2)/8)) ≈(1/2)−((0.109791)/(ln 2))=0.341605