Question

Equações Exponenciais
i-) (√1/2)^x=1/128
j-) ³√3x= 3^x-8

Answer 1

(√2^-1)^x=128^-1
(2^-x/2)=(2^7)^-1

Answer 2

i)
$( \sqrt{ \frac{1}{2} } )^x= \frac{1}{128} \\ \\ ( \sqrt{2^{-1}} )^x= \frac{1}{2^7} \\ \\ 2^{- \frac{x}{2}}=2^{-7} \\ \\ - \frac{x}{2} =-7 \\ \\ -x=-14 \\ x=14$

j)
$\sqrt[3]{3^x} =3^{x-8} \\ \\ 3^{ \frac{x}{3} }=3^{x-8} \\ \\ \frac{x}{3} =x-8 \\ \\ x=3x-24 \\ x-3x=-24 \\ -2x=-24 \\ 2x=24 \\ x=24\div2 \\ x=12$