How do you evaluate log_27 (1/3)?

1 Answer
Aug 4, 2016

log_27 (1/3) = -1/3

Explanation:

By definition log is the inverse of exponentiation and vice versa for any base b. That is:

log_b (b^x) = x for all Real values of x

b^(log_b x) = x for all x > 0

The change of base formula tells us that for any a, b, c > 0 with a != 1 and c != 1:

log_a b = (log_c b) / (log_c a)

So we find:

log_27 (1/3) = (log_3 (1/3)) / (log_3 27) = (log_3 3^(-1)) / (log_3 3^3) = -1/3