In a logarithmic regression, does it matter which letter is assigned to which coefficient?

Question

I have seen a logarithmic function written as: $$y = a + b \ln(x).$$ For example, here.

But also, I've seen it written as: $$ y = a \ln(x) + b .$$ For example, here.

Is there a reason to assign a certain letter to a certain coefficient? Does it matter which one is assigned to which?

Answer 1

They are just algebraic symbols. It doesn't matter.

For familiarity, you might like to use $m$ and $c$ as $Y=mX+c$ is a common notation where $m$ represents the gradient and $c$ represents the intercept.

Hence some might prefer to write $$y=m\ln x + c$$

However, feel free to use other symbols as long as they do not cause confusion.

Answer 2

No, the following sets of function are equal $$ \{a\ln x+b\,|\,a,b\in \mathbb R\}=\{a+b\ln x\,|\,a,b\in \mathbb R\} $$