4.6.5: Repeated division.

(a)

Start with the number n = 54527. Divide n by 5 and round the result down to an integer. Keep repeating the division and rounding step until the resulting number is less than 5. How many divisions are performed? You can use a calculator for this problem, but you should not have to actually perform all of the divisions.

(b)

Start with the number n = 54527. Divide n by 5 and round the result up to an integer. Keep repeating the division and rounding step until the resulting number is less than 5. How many divisions are performed? You can use a calculator for this problem, but you should not have to actually perform all of the divisions.

(c)

Suppose that you have a calculator that performs the log function but you do not know the base of the log. How can you use your calculator to solve the two problems above?