Question #aec5e Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer sente Dec 11, 2016 #x = e^e-1~~14.154# Explanation: Using the property that #e^ln(x) = x#, we have #ln(ln(x+1))=1# #=> e^(ln(ln(x+1))) = e^1# #=> ln(x+1) = e# #=> e^(ln(x+1)) = e^e# #=> x+1 = e^e# #:. x = e^e-1~~14.154# 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 1757 views around the world You can reuse this answer Creative Commons License