Question

What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

Answer 1

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.