Question

Equação exponencial
(1/9)^x=27^x/2

Answer 1

(1/9)^x=27^x/2
(1/3^2)= 3^3(x/2)
    3^-2= 3^3(x/2)
base igual : agora resolver os expoentes
       
        -2 = 3x/2
         x = - 4/3
         

Answer 2

Ae,

aplique a propriedade da exponenciação:

$\left( \dfrac{1}{9} \right)^x=27^{ \tfrac{x}{2} }\\\\\left( \dfrac{1}{3^2}\right)^x=(3^3)^{ \tfrac{x}{2}}\\\\(3^{-2})^x=3^{ \tfrac{3}{2}x}\\\\3^{-2x}=3^{ \tfrac{3}{2}x } \\\\\not3^{-2x}=\not3^{ \tfrac{3}{2}x } \\\\-2x= \dfrac{3}{2} \\\\2\cdot(-2x)=3\\-4x=3\\\\x=- \dfrac{3}{4}\\\\\\\text{S}=\left\{- \dfrac{3}{4} \right\}$   
Tenha ótimos estudos ;P