Equal spaced points in a logarithmic graph

Question

I am plotting a graph with the x-axis as logarithmic. I want to select 10 point that are equally spaced in a logarithm scale. How can I determine the values if we have the range from 100 to 10000?

Answer 1

Well you know that $10^1$, $10^2$, placed $10^3$ are all placed evenly on a logarithmic scale. It turns out that the exponential functions and logarithmic functions are inverses of one another (generally speaking).

Basically, since $100$ = $10^2$ and $10000 = 10^4$, you have to pick 10 numbers that are evenly spaced between 2 and 4. For example, lets choose:

$3.1$, $3.2$, $3.3$, ..., $4.0$ are all separated by a distance of $0.1$.

$10^{3.1}$ is the same distance from $10^{3.2}$ as $10^{3.4}$ is from $10^{3.5}$ on the logarithmic scale.