Suppose we solve $$\frac{dy}{dx} = \frac{1 + y}{2 + x} .$$ Which can be written as the following and integrating both sides w.r.t. $y$ and $x$: $$\int\frac{1}{1 + y}dy = \int\frac{1}{2 +x}dx ,$$ we get $$\ln(1+y) = \ln(2+x) + C$$ One of the book says:
It's convenient to write the constant $C$ as the logarithm of some other constant $A$: $$ \ln(1+y) = \ln(2+x) + \ln(A) \implies \ln A(2 + x)$$ $$ \therefore (1 + y) = A(2 + x)$$
Question: Why is it "convenient to write the constant $C$ as the logarithm of some other constant $A$"? What liberty do we have to write $\ln(A)$ instead of just $C$? I think I am unaware of what a logarithm of a constant is. I mean the significance of it.