Question

What logarithmic function represents the data in the table?

x f(x)
216 3
1296 4
7776 5

Choices:

f(x)=logx5

f(x)=6logx

f(x)=log6^x

f(x)=log6x

Answer 1

The correct answer among the choices provided is the fourth option. The logarithmic function f(x)=log(base 6)x represents the data in the table. Log is the value that one can get to express a number to a certain power. It is solved through finding the pattern using the given values,
6^3 = 216
6^4 = 1296
6^5 = 7776

Answer 2

216 =6^3
1,296 = 6^4
7,776 = 6^5
x = 6^f(x)
log x = log 6^f(x) = f(x)log 6
f(x) = log x / log 6 =
`log_6x`