Question Number 100916 by 175 last updated on 29/Jun/20

solve the eqution :  ((2 + x)/(12 + 4x)) = ((1/2))^x        .,x =2

Answered by 1549442205 last updated on 30/Jun/20

⇔2^x −((12+4x)/(2+x))=0⇔2^x −(6/(x+2))−4=0(∗)  ⇒x=2.421432378  putting f(x)=2^x −(6/(x+2))−4⇒f ′(x)=  2^(x ) ln2+(6/((x+2)^2 ))>0∀x∈(−∞;+∞).so  f(x) is increasing function on (−∞;+∞)  Hence,x=2.421432378 is unique root  of the equation (∗)