Answer:
The logarithmic function modeled by the given table:
f(x) = log₃x
Explanation:
Given Table:
x f(x)
9 2
27 3
81 4
We can see that x increases as powers of 3. And f(x) is the power.
We assume that f(x) = log₃x
Checking using the table:
for x = 9
f(x) = log₃9 = 2
for x = 27
f(x) = log₃27 = 3
for x = 81
f(x) = log₃81 = 4
Hence proved.