Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
let [tex]log_{125}[/tex] 5 = n, then
5 = [tex]125^{n}[/tex]
note that 125 = 5³ ⇒ [tex](5^3) ^{n}[/tex] = [tex]5^{3n}[/tex]
Since bases are equal ( both 5) equate the exponents
3n = 1 ( divide both sides by 3 )
n = [tex]\frac{1}{3}[/tex]
