Answer: [tex]f(x)=\log_5x[/tex]
Step-by-step explanation:
Given table: x f(x)
25 2
125 3
625 4
Here, we can write x as powers of 5 such that
[tex]25=5^2\\125=5^3\\625=5^4\\\Rightarrow\ f(x)= 5^{f(x)}[/tex]
Now, Taking log on both sides, we get
[tex]\log\ x=\log5^{f(x)}\\\Rightarrow\ \log\ x=f(x)\log5....[\log(a)^m=m\log(a)]\\\Rightarrow\ f(x)=\frac{\log\ x}{\log5}\\\Rightarrow\ f(x)=\log_5x......[\log_ab=\frac{\log\ b}{\log\ a}][/tex]
Therefore, A base-log function [tex]f(x)=\log_5x[/tex] represents data in the table
