# 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 a^{1} = 3

So the base is 3

f(x) = log_{3}(x)

If x = 9

log_{3}(9) = log_{3}(3^{2}) = 2

Therefore, the logarithmic function f(x) = log_{3}(x) represents the data in the table.

## 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) = log_{3}(x).

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