Question

9^(2x) • 27^(3-x) = 1/9

Answer 1

Answer:

$\huge\boxed{x=-11}$

Step-by-step explanation:

$9^{2x}\cdot27^{3-x}=\dfrac{1}{9}\\\\9=3^2;\ 27=3^3;\ \dfrac{1}{9}=3^{-2}\\\\\text{therefore}\\\\(3^2)^{2x}\cdot(3^3)^{3-x}=3^{-2}\qquad|\text{use}\ (a^n)^m=a^{nm}\\\\3^{2\cdot2x}\cdot3^{3(3-x)}=3^{-2}\\\\3^{4x}\cdot3^{9-3x}=3^{-2}\qquad|\text{use}\ a^n\cdot a^m=a^{n+m}\\\\3^{4x+9-3x}=3^{-2}\\\\3^{x+9}=3^{-2}\iff x+9=-2\qquad|\text{subtract 9 from both sides}\\\\x+9-9=-2-9\\\\x=-11$