What logarithmic function represents the data in the table?
f(x) = log_x5
f(x) = 6 log_x5
f(x) = log6^x
f(x) = log₆x

x	f(x)
216	3
1296	4
7776	5

Solution:

By inspection,

f(x) = log₆ x represents the data in the table.

If x = 216, f(x) = log₆x

⇒ f(216) = log₆216

f(216) = log₆6³ = 3log₆6

f(216) = 3

If x = 1296, f(x) = log₆x

⇒ f(1296) = log₆1296

f(1296) = log₆6⁴ = 4log₆6

f(1296) = 4

If x = 7776, f(x) = log₆x

⇒ f(7776) = log₆7776

f(7776) = log₆6⁵ = 5log₆6

f(1296) = 5

The logarithmic function, f(x) = log₆x, represents the data in the table.

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What logarithmic function represents the data in the table?

Summary:

The logarithmic function, f(x) = log₆x, represents the data in the table.