What logarithmic function represents the data in the table?

x	1	3	9
f(x)	0	1	2

Solution:

Let us assume the columns (1, 0) (3, 1) (9, 2)

f(x) = log_a(x)

Where log_a is logarithm in base a

If x = 1, we get

log_a(1) = 0

If x = 3, we get

log_a(3) = 1

Here a¹ = 3

So the base is 3

f(x) = log₃(x)

If x = 9

log₃(9) = log₃(3²) = 2

Therefore, the logarithmic function f(x) = log₃(x) represents the data in the table.

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What logarithmic function represents the data in the table?

x	1	3	9
f(x)	0	1	2

Summary:

The logarithmic function which represents the data in the table x, f(x))= (1, 0) (3, 1) (9, 2) is f(x) = log₃(x).