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.