Answer: \(f(x)=\log_5x\)
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
\(25=5^2\\125=5^3\\625=5^4\\\Rightarrow\ f(x)= 5^{f(x)}\)
Now, Taking log on both sides, we get
\(\log\ x=\log5^{f(x)}\\\Rightarrow\ \log\ x=f(x)\log5....[\log(a)^m=m\log(a)]\\\Rightarrow\ f(x)=\frac{\log\ x}{\log5}\\\Rightarrow\ f(x)=\log_5x......[\log_ab=\frac{\log\ b}{\log\ a}]\)
Therefore, A base-log function \(f(x)=\log_5x\) represents data in the table
