Convert a linear scale to a logarithmic scale
Solution 1:
let $f(n)$ be the log function of n.
So a general log function can be written as $f(n)=k\log n +c$
where $k$ and $c$ are constants
$\implies 255=k\log {10^6}+c$
and $0=k\log {1}+c$
here is to the base 10
so $c=0$ and $k=255/6$
or here you can use any base and different values of k
so that $f(n)=\frac {255 \log n}{6}$ if the base is 10.