How do you evaluate log_27 (1/3)?
1 Answer
Aug 4, 2016
log_27 (1/3) = -1/3
Explanation:
By definition
log_b (b^x) = x for all Real values ofx
b^(log_b x) = x for allx > 0
The change of base formula tells us that for any
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