\(\left(\dfrac{2}{3}\right)^{x+2}+\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{20}{27}\)
=\(\dfrac{2}{3}.\left(\dfrac{2}{3}\right)^{x+1}+\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{20}{27}\)
=>\(\left(\dfrac{2}{3}\right)^{x+1}.\left(\dfrac{2}{3}+1\right)=\dfrac{20}{27}\)
=\(\left(\dfrac{2}{3}\right)^{x+1}.\left(\dfrac{5}{3}\right)=\dfrac{20}{27}\)
=>\(\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{4}{9}\)=>\(\left(\dfrac{2}{3}\right)^{x+1}=\left(\dfrac{2}{3}\right)^2\)
=>\(x+1=2=>x=1\)