Question

Complete the table.

x

1 ___

7 ___

49 ___

log7 x
___ -1

___ -2

A.) 1/2

B.) 0

C.) 7

D.) 1

E.) 2

F.) 49

G.) 1/7

H.) 1/49

Answer 1

x, log7(x)

1, 0 (B)

7, 1 (D)

49, 2 (E)

1/7, -1 (G)

1/49, -2 (H)

Explanation:

Powers of 7 are ...

7^-2 = 1/7^2 = 1/49

7^-1 = 1/7^1 = 1/7

7^0 = 1

7^1 = 7

7^2 = 49

The log (base 7) of the number on the right is the exponent on the left. That is ...

log7(7) = log7(7^1) = 1

log7(1/49) = log7(7^-2) = -2