How do you solve #log_5(5^(6n+1))=13#? Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer seph Oct 24, 2016 #n = 2# Explanation: #log_5 5^(6n + 1) = 13# #log_n m^x = x log_n m# #=> (6n + 1)log_5 5 = 13# #log_n n = 1# #=> 6n + 1 = 13# #=> 6n = 12# #=> n = 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 1598 views around the world You can reuse this answer Creative Commons License