Question

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

Answer 1

Required logarithmic function is :

`f\left(x\right)=\log_3\left(x\right)`

Explanation:

We have been fiven that table for the logarithmic function is:

x f(x)

9 2

27 3

81 4

which can be rewritten as:

x f(x)

3^2 2

3^3 3

3^4 4

Which are basically powers of 3

So we can use logarithmic function as

`\log_3\left(9\right)=\log_3\left(3^2\right)=2\log_3\left(3\right)=2(1)=2`

Hence required logarithmic function is :

`f\left(x\right)=\log_3\left(x\right)`