Question

5) Determine o conjunto verdade do log x 16 = -2​

Answer 1

Explicação passo a passo:

$\sf{\log_{x} (16) = - 2}$

$\sf{x^{-2} = 16}$

$\sf{\dfrac{1}{x^2} = 16}$

$\sf{1 = x^2 \times 16}$

$\sf{1 = 16x^2}$

$\sf{16x^2 = 1}$

$\sf{x^2 = \dfrac{1}{16}}$

$\sf{x = \sqrt{\dfrac{1}{16}}}$

$\sf{x = \dfrac{\sqrt{1}}{\sqrt{16}}}$

$\sf{x = \dfrac{1}{4}}$

$\boxed{\sf{S = \left\{ \: \dfrac{1}{4}\right\ \}}}$