How do you find the exact value of #log_5 75-log_5 3#? Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer Alan N. Jan 7, 2017 #log_5 75 - log_5 3 = 2# Explanation: Remember that #log_a b - log_a c = log_a (b/c)# #:. log_5 75 - log_5 3 = log_5 (75/3) = log_5 25# Let #x = log_5 25# #:. 5^x = 25# #-> 5^x = 5^2# Equating indices: #x=2# Hence: #log_5 75 - log_5 3 = 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 7881 views around the world You can reuse this answer Creative Commons License