How do you solve #(e^4)^x * e^(x^2) = e^12#? Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer Noah G Jul 8, 2016 #e^(4x) xx e^(x^2) = e^12# By the rule #a^n xx a^m = a^(n + m)# #x^2 + 4x - 12 = 0# #(x + 6)(x - 2) = 0# #x = -6 and 2# Hopefully this helps! 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 5886 views around the world You can reuse this answer Creative Commons License