Question

Resolva as equações exponenciais a seguir:
a) ³√4× + 1 = 1

b) (1/3)× = ⁴√27

Answer 1

a) ³√4× + 1 = 1
4^x+1/3 = 4^0
x+1/3 = 0
x+1 = 0
x = -1 ✓

b) (1/3)× = ⁴√27
(1/3)^x = ⁴√3³
(1/3)^x = 3^3/4
(1/3)^x = (1/3)^-3/4
x = -3/4 ✓

Answer 2

Explicação passo-a-passo:

a)

$\sqrt[3]{4^{x+1}} =1\\ \\ 4^{x+1\over3}=4^0\\ \\ cancela~~4\\ \\ {x+1\over3}=0\\ \\ x+1=0\\ \\ x=-1\\ \\ S=\{-1\}$

b)

$({1\over3})^x=\sqrt[4]{27} \\ \\ 3^{-x}=\sqrt[4]{3^3} \\ \\ 3^{-x}=3^{3\over4}\\ \\ cancela~~o~~3\\ \\ -x={3\over4}\\ \\ x=-{3\over4}\\ \\ S=\{-{3\over4}\}$