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# What logarithmic function represents the data in the table?

f(x) = log_{x}5

f(x) = 6 log_{x}5

f(x) = log6^{x}

f(x) = log_{6}x

x | f(x) |

216 | 3 |

1296 | 4 |

7776 | 5 |

**Solution:**

By inspection,

f(x) = log_{6 }x represents the data in the table.

If x = 216, f(x) = log_{6}x

⇒ f(216) = log_{6}216

f(216) = log_{6}6^{3} = 3log_{6}6

f(216) = 3

If x = 1296, f(x) = log_{6}x

⇒ f(1296) = log_{6}1296

f(1296) = log_{6}6^{4} = 4log_{6}6

f(1296) = 4

If x = 7776, f(x) = log_{6}x

⇒ f(7776) = log_{6}7776

f(7776) = log_{6}6^{5} = 5log_{6}6

f(1296) = 5

The logarithmic function, f(x) = log_{6}x, represents the data in the table.

## What logarithmic function represents the data in the table?

**Summary:**

The logarithmic function, f(x) = log_{6}x, represents the data in the table.

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