Answer:
B. 4
Step-by-step explanation:
Given :
[tex]log_x(\frac{1}{8})=-\frac{3}{2}[/tex]
The logarithm function can be converted to an exponential function as
[tex][\log_ab=c][/tex] can be expressed as [tex][a^c=b][/tex]
Similarly for the given expression
[tex]log_x(\frac{1}{8})=-\frac{3}{2}[/tex]
We can write,
[tex]x^{-\frac{3}{2}}=\frac{1}{8}[/tex]
Using property of negative exponents [tex][a^{-b}=\frac{1}{a^b}][/tex]
[tex]\frac{1}{x^{\frac{3}{2}}}=\frac{1}{8}[/tex]
So we can write that as:
[tex]x^{\frac{3}{2}}=8[/tex]
Writing the exponents in radical form as [tex]a^{\frac{b}{c}}=(\sqrt[c]{a})^b[/tex]
[tex](\sqrt{x})^3=8[/tex]
Taking cube root both sides to remove the cube.
[tex]\sqrt[3]{(\sqrt{x})^3}=\sqrt[3]{8}[/tex]
[tex]\sqrt x=2[/tex]
Squaring both sides to remove square root.
[tex](\sqrt x)^2=2^2[/tex]
∴ [tex]x=4[/tex]
