>>11219983for y = 2^x if you increase the input (x) by 1 you double the output. y = 2^x is identical to log base 2 (y) = x (in other words if you increase x here by 1, and rearrange for y, y is doubled.. same thing).
but when you rearrange like that, you can think of y as the input, and x as the output instead which means that in order to increase x by 1 you need to double the input. if log was base 3 you would need to triple the input.
this is useful because sometimes you get exponential functions that are easier to graph on log graphs (which then may appear linear, as the log/exponential cancels out) which will express the same sentiment as a regular graph but in a more compact way. in control systems you use log graphs all the time for roughly this purpose.
exponential functions are ubiquitous throughout engineering and therefore logs are too, because the derivative of e^x is e^x which is an incredibly useful to make the algebra for difficult problems manageable.
