Question

Calcule logaritmo
Log1/2 3raiz 4

Answer 1

Propriedades que utilizarei:

$\left(\dfrac{a}{b}\right)^{n}=\left(\dfrac{b}{a}\right)^{-n}\\\\\\\sqrt[b]{x^{a}}=x^{a/b}$
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$log_{(\frac{1}{2})}(\sqrt[3]{4})=x$

Pela definição de logaritmos, temos que:

$\left(\dfrac{1}{2}\right)^{x}=\sqrt[3]{4}\\\\\\\left(\dfrac{1}{2^{1}}\right)^{x}=\sqrt[3]{2^{2}}$

Invertendo 1/2¹ e transformando a raiz em potência:

$(2^{-1})^{x}=2^{2/3}\\2^{-x}=2^{2/3}$

Bases iguais, iguale os expoentes:

$-x=\dfrac{2}{3}\\\\\\\boxed{\boxed{x=-\dfrac{2}{3}}}$