If I go to the left that distance twice this will be the same thing as dividing by 10 twice dividing by 10, dividing by 10 which is the same thing as multiplying by, well one way to think of it 1/10² or dividing by 10² is another way of thinking about it and so that might make a little you know that might be, hopefully, a little bit intuitive and you can already see why this is valuable we can already, on this number line, plot a much broader spectrum of things than we can on this number line we can go all the way up to a 100 and then we even get some nice granularity if we want to go down to one tenth and one hundredth here we don't get the granularity at small scales and we also don't get to go to really large numbers and if we go a little distance more we get to 1000 and then we get to 10000 so on and so forth so we can really cover a much broader spectrum on this line right over here but what's also neat about this is that when you move a fixed distance so when you move a fixed distance on this linear number line you are adding or subtracting that amount so if you move that fixed distance you are adding to, to the right if yo go to the left you're subtracting to when you do the same thing on a logarithmic number line and this is true of any logarithmic number line you will be scaling by a fixed factor and one way to think about what that fixed factor is is this idea of exponents so if you wanted to say