Question

logaritmo 3raiz3 na base 3 =x

Answer 1

Olá.

$\mathsf{log^{3\sqrt{3}}_{3} = x}$

Lembrando que:

$\boxed{\mathsf{log_{b}^{a} = c \to b^{c} = a}}$

Resolução:

$\mathsf{3^{x} = 3\sqrt{3}} \\ \\ \mathsf{3^{x} = 3 \times 3^{\frac{1}{2}}} \\ \\ \mathsf{3^{x} = 3^{1 + \frac{1}{2}}} \\ \\ \mathsf{3^{x} = 3^{\frac{3}{2}} \to cortando \: as \: bases} \\ \\ \mathsf{x = \frac{3}{2}}$

Bons estudos.

Answer 2

log₃   3√3 = x

3ˣ = 3√3

3ˣ = 3. 3¹/²

x = 1 + 1/2

x = 3/2