The discussion centers on the mathematical expression e^x represented as the infinite series Ʃ[k=0,∞] x^k/k!. Participants confirm the validity of the logarithmic transformation ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!), leading to the conclusion x = ln(Ʃ[k=0,∞] x^k/k!). However, the practical utility of this transformation is questioned, with some participants expressing uncertainty about its relevance in calculus.
PREREQUISITESStudents and educators in calculus, mathematicians interested in series convergence, and anyone looking to deepen their understanding of exponential and logarithmic functions.
Sure, but how useful it is, I don't know.GreenPrint said:Sense e^x=Ʃ[k=0,∞] x^k/k!
then
ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!)
x = ln(Ʃ[k=0,∞] x^k/k!)
is this true?
Mark44 said:Sure, but how useful it is, I don't know.
I sense that you don't understand the difference between sense and since.