Question

-ln x = t/T + C
how do i simplify?

Answer 1

\[\ln (x) = - ( t/T +C )\]\[x= e ^{-t/T +C}\]\[x= e ^{-t/T}e ^{C}\]


Now let e^C =A ( it is just a constant )

so

\[x= Ae ^{-t/T}\]

Answer 2

edit: the second line should be :\[e ^{-t/T}e ^{-C}\]

but nevertheless e^(-C) is still a positive constant and can be replaced by "A" ( another constant )

Answer 3

Thank you!!