If log(1/b) a=-3, what are the possible integer values for a and b?

Answer 1

log_1/b (a) = -3

Rewrite in the exponential form:

(1/b)^-3 = a

1^-3/b^-3 = a

1/b³ = a

b³ = 1/a

b = ³√(1/a)

Possible integer pairs (a, b): 1, 1; 2, (1/2)^1/3; 3, (1/3)^1/3; 4, (1/4)^1/3; etc.