If Logx (1 / 8) = - 3 / 2, then x is equal toA. - 4B. 4C. 1 / 4

Answer:B. 4Step-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]