Answer:
x = 5
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex]
given
[tex]log_{x}[/tex] [tex]\frac{1}{125}[/tex] = - 3 , then [tex]\frac{1}{125}[/tex] = [tex]x^{-3}[/tex]
note that [tex]\frac{1}{125}[/tex] = [tex]5^{-3}[/tex] , so
[tex]5^{-3}[/tex] = [tex]x^{-3}[/tex]
since the exponents are equal, both - 3 then the bases are equal , so
x = 5
