What logarithmic function represents the data in the table? x f(x) 25 2 125 3 625 4

Asked by maham237 @ in Mathematics viewed by 477 People

What logarithmic function represents the data in the table?
x f(x)

25 2
125 3
625 4

Answered by maham237 @


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


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