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 (∗)