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1 vote
What logarithmic function represents the data in the table?

x f(x)

25 2
125 3
625 4

2 Answers

6 votes
The logarithmic function that represents the data in the table is given by f(x) =
\log_5x
User Mohammed Javed
by
7.9k points
4 votes

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

User Jerry
by
7.5k points

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