Question

If Log x (1 / 8) = - 3 / 2, then x is equal to. A. - 4 B. 4 C. 1 / 4 D: 0

Answer 1

$log_{x}(1/8)=-3/2$

This is equal to...

$x^{-3/2}=1/8$

We want "x" so we need to isolate it using laws of exponents...

$x^{(-1)(3/2)}=1/8$

$x^{3/2}=8$ because $x^{-a}=1/x^{a}$

$x=\sqrt[3]{8^{2}}$ because $x^{a/b}=\sqrt[b]{x^{a}}$

x = 4

answer: B