Question

What logarithmic function represents the data in the table?

x f(x)

25 2
125 3
625 4

Answer 1

The logarithmic function that represents the data in the table is given by f(x) =
`\log_5x`

Answer 2

Answer:
`f(x)=\log_5x`

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)=(\log\ x)/(\log5)\\\Rightarrow\ f(x)=\log_5x......[\log_ab=(\log\ b)/(\log\ a)]`

Therefore, A base-log function
`f(x)=\log_5x` represents data in the table