How do you evaluate #log_9 (1/3)#? Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer Alan N. Aug 31, 2016 #-1/2# Explanation: #log_9(1/3) = log_9 3^-1 = -log_9 3# #= -log_9 9^(1/2)# #= -1/2# To check answer #log_9 (1/3) = ln(1/3)/ln9# #~= -1.09861/2.19723 ~=-1/2# Answer link Related questions What is a logarithm? What are common mistakes students make with logarithms? How can a logarithmic equation be solved by graphing? How can I calculate a logarithm without a calculator? How can logarithms be used to solve exponential equations? How do logarithmic functions work? What is the logarithm of a negative number? What is the logarithm of zero? How do I find the logarithm #log_(1/4) 1/64#? How do I find the logarithm #log_(2/3)(8/27)#? See all questions in Logarithm-- Inverse of an Exponential Function Impact of this question 1244 views around the world You can reuse this answer Creative Commons License