Comparing growth rates? Determine which of the two functions grows faster, or state that they have comparable growth rates. ln xand log 10

Solution Step 1 In this problem we have to determine which of the two functions ln xand log x, grows fast10 than the other otherwise we have to state the comparable growth rates. Suppose f and gare functions such that limf(x) = , limg(x) = x x Enough to prove:lim g(x) = 0which means f grows faster than gas x x f(x) l'Hôpital's Rule: Suppose that we have one of the following cases, lim f(x)= or lim f(x)= ± xa g(x) 0 xa g(x) ± Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim = lim xa g(x) xa gx)