Answer:
B
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{x}[/tex] ([tex]\frac{1}{8}[/tex] ) = - [tex]\frac{3}{2}[/tex], then
[tex]\frac{1}{8}[/tex] = [tex]x^{-\frac{3}{2} }[/tex]
Square both sides
[tex]\frac{1}{64}[/tex] = [tex]x^{-3}[/tex]
[tex]4^{-3}[/tex] = [tex]x^{-3}[/tex] ⇒ x = 4 → B
