The ranking of growth rates given in the text applies for x→∞. However, these rates may not be evident for small values of x. For example, an exponential grows faster than any power of x. However, for 1 < x < 19,800, x² is greater than e^x/1000. For the following pairs of functions, estimate the point at which the faster-growing function overtakes the slower-growing function (for the last time).

a. ln³ x and x^0.3 

b. 2^x/100 and x³

c. x^x/100 and e^x 

d. ln¹⁰ x and e^x/10