If $A$ is equal to $\log(B)$, is $A$ proportional to $B$?

Question

Simple question, but I'm doubting myself here.

If $A = \log(B)$, is $A \propto B$?

I understand proportionality as: If $A$ is proportional to $B$, $A$ increases as $B$ increases.

Is this true?

Answer 1

You could say $A$ is a monotonous increasing function of $B$, i.e. if $A$ increases then so does $B$. You cannot say they are proportional since, according to the definition on Wikipedia, this means there is a constant ratio between the two quantities, i.e $A=kB$. This does not hold here.