Question

resolva as equações exponenciais : raiz (1/2) ^3x-2 =(1/2)^-4x vezes 2^-x+4

Answer 1

Aplicando propriedades de potencias e raízes

           $\sqrt{ ( \frac{1}{2}) ^{3x-2} } = ( \frac{1}{2}) ^{-4x} . 2^{-x+4} \\ \\ ( 2^{-1} ) ^{ \frac{3x-2}{2} } =( 2^{-1}) ^{-4x} . 2^{x-4} \\ \\ 2^{- \frac{3x-2}{2} } = 2^{4x+x-4} \\ \\ - \frac{3x-2}{2} =5x-4 \\ \\ -3x+2=10x-8 \\ \\ -3x-10x=-8-2 \\ \\ -13x=-10 \\ \\ x= \frac{10}{13}$