Question

Preciso de ajuda para resolver equações exponenciais. Me ajudem na seguinte equação : $( \frac{3}{5})^{x}=( \frac{25}{9} ) ^{x+1}$

Answer 1

$\left(\dfrac{3}{5}\right)^x=\left(\dfrac{25}{9}\right)^{x+1}\\\\ \left[\left(\dfrac{5}{3}\right)^{-1}\right]^x=\left[\left(\dfrac{5}{3}\right)^2\right]^{x+1}\\\\ \left(\dfrac{5}{3}\right)^{-x}=\left(\dfrac{5}{3}\right)^{2x+2}\\\\ -x=2x+2\\\\3x=-2\\\\\boxed{x=-2}\\\\ S\{-\dfrac{2}{3}\}$

Answer 2

$(\frac{3}{5})^x=(\frac{25}{9})^{x+1} \\ \\ (\frac{3}{5})^x=[(\frac{3}{5})^{-2}]^{x+1} \\ \\ (\frac{3}{5})^x=(\frac{3}{5})^{-2x-2} \\ \\ x=-2x-2 \\ 3x=-2 \\ \\ \boxed{x=-\frac{2}{3}}$