Question

Explain s= k ln w

Answer 1

Logs are a way to convert large number so much smaller numbers:
$$
s=k\ln w
$$
means
$$
\large{
e^{s}=e^{k\ln w}\\
e^{s}=e^ke^{\ln w}\\
e^{s}=e^kw\\
\implies w=\cfrac{e^s}{e^k}
}
$$
So \(w\) represents not \(s\), but rather \(\large e^s\), which is very very large for large s. So this shows how logs are a way to write large numbers in smaller scales. The factor \(k\) just "tweaks" the log. Hence, \(\large e^k\) "tweaks" the antilog of \(\ln w\), which is simply \(w\).

Note that "e" is the antilog for this case.