how does this ln equation equal this

[sozener1]

how does
lny= -lnx+c=-lnx+lnA=ln(A/x)

become this like shown in the attachement

 

[stapel]

how does
lny= -lnx+c=-lnx+lnA=ln(A/x)

become this like shown in the attachement

The change was made to enable simplification into one log term. Since C is just some number, then C = ln(A) for some A such that e^C = A. Once C is converted to ln(A), the two log terms can be combined.

 

[HallsofIvy]

Strictly speaking, in order that C= ln(A), A would have to be positive but the correct integral of 1/x is ln|x|, not ln(x), anyway.