In order to solve the equation we should take the natural logarithm of both sides of the equation (the goal is to remove the variable from the exponent)ln(4^(2x+1))=ln(3^(x−2))
(2x+1)ln(4)=(x-2)ln(3)
2x*ln(4)+ln(4)=xln(3)-2ln(3)
2x*ln(4)-xln(3)=-ln(4)-2ln(3)
x(2ln(4)-ln(3))=-ln(4)-2ln(3)
x=-ln(4)-2ln(3)/(2ln(4)-ln(3))