let me do it right over here so you take the log of 7 it is going to be roughly 0.85 so 7 is just going to be squeezed in roughly right over there so a couple of neat things you already appreciated one, we can fit more on this logarithmic scale and, as i did with the video with Vi Hart where she talked about how we perceive many things with logarithmic scales so that is actually a good way to even understand some of human perception but the other really cool thing is when we move a fixed distance on this logarithmic scale we are multiplying by a fixed constant now the one kind of strange thing about this and you might have already noticed here is that we don't see the numbers lined up the way we normally see them there is a big jump from 1 to 2 then a smaller jump from 3 to 4 then a smaller jump from that from 3 to 4 then even smaller from 4 to 5 then even smaller from 5 to 6 and then 7, 8, 9 7 is gonna be right in there it gets squeezed squeezed squeezed in tighter and tighter and tighter and then you get 10 and then you get another big jump because once again if you wanna get to 20, you just have to multiply by 2 you just have to multiply by 2 again so this distance again gets us to 20 if you go this distance over here that will get you to 30 cause you're multiplying by 3 so this right over here is our times 3 distance so if you do that again, if you do that distance then that gets you to 30 you're multiplying by 3 and then you could plot the whole same thing over here again but hopefully this gives you a little bit more intuition of why logarithmic number lines