Re:The Oxford maths interview, shaking up admissions
by dastbe on Friday March 04, 2016 @08:58AM
(#11223688)
So I would argue the easiest way to plot log log x is to parameterize the x domain.
For f x = log x where log has base b, we know that f b^0 = 0, f b^1 = 1, etc. what does g x = log log x look like? Well, we know log x is undefined for x < 0, which implies g is undefined for x < b^0 = 1, or b^b^0. More generally, you can say when f x = y, g b^x = y. So we know that g intercepts 0 at b^b^0 = b. You could do this for several more points for y = 1, y = 2, and so on, or you could draw a graph of log x and just relabel the x-axis to be 1) shifted by 1 with the x-intercept at b and 2) scaled logarithmically.
For f x = log x where log has base b, we know that f b^0 = 0, f b^1 = 1, etc. what does g x = log log x look like? Well, we know log x is undefined for x < 0, which implies g is undefined for x < b^0 = 1, or b^b^0. More generally, you can say when f x = y, g b^x = y. So we know that g intercepts 0 at b^b^0 = b. You could do this for several more points for y = 1, y = 2, and so on, or you could draw a graph of log x and just relabel the x-axis to be 1) shifted by 1 with the x-intercept at b and 2) scaled logarithmically.