Question

resolva as equações exponenciais e determine o conjunto solução . a) 2× = 8 b) 2×=64 c) 25×= 125 d) 7× =343

Answer 1

Olá

Para encontrar expoentes em equações exponenciais, devemos igualar as bases

Quando as bases forem iguais, iguale os expoentes

1° caso:

$2^{x}=8\\\\\\ 2^{x}=2^{3}\\\\\\ \boxed{x=3}~~\checkmark$

$\boxed{S=\{3\}~|~x \in\mathbb{R}}$

2° caso:

$2^{x}=64\\\\\\ 2^{x}=2^{6}\\\\\\ \boxed{x=6}~\checkmark$

$\boxed{S=\{6\}~|~x\in\mathbb{R}}$

3° caso:

$25^{x}=125\\\\\\ (5^{2})^{x}=5^{3}\\\\\\ 5^{2x}=5^{3}\\\\\\ 2x = 3\\\\\\ \boxed{x=\dfrac{3}{2}}~~\checkmark$

$\boxed{S=\left\{\dfrac{3}{2}\right\}~|~x\in\mathbb{R}}$

4° caso:

$7^{x}=343\\\\\\ 7^{x}=7^{3}\\\\\\ \boxed{x=3}~~\checkmark$

$\boxed{S=\{3\}~|~x\in\mathbb{R}}$