Question

03. A equação (0,5)^x = 1/16 em R vale: * 2 pontos a) {-4} b) {4} c) {-2} d){2} e) {-1}

Answer 1

Explicação passo-a-passo:

$\sf (0,5)^x=\dfrac{1}{16}$

$\sf (2^{-1})^x=2^{-4}$

$\sf 2^{-x}=2^{-4}$

Igualando os expoentes:

$\sf -x=-4$

$\sf x=4$

$\sf S=\{4\}$

Letra B

Answer 2

$\sf{0,5=\dfrac{5}{10}=\dfrac{\diagup\!\!\!\! 5}{ \diagup\!\!\!\!5\cdot2}=\dfrac{1}{2}=2^{-1}}$

$\sf{0,5^x=1/16}\\\sf{(2^{-1})^x=2^{-4}}\\\sf{2^{-x}=2^{-4}}\\\sf{-x=-4\cdot(-1)}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=4}}}}}$

$\large\boxed{\boxed{\boxed{\boxed{\sf{\maltese~~alternativa~~b}}}}}$