Powers

Save both functions into the file powers.py.

1. Write the function powers_1() that takes two positive integers, x and maxn, and returns the average of the sequence of powers of x less than or equal to maxn. Examples:

   >>> round(powers_1 (2, 100), 2)
   18.14
   >>> round(powers_1 (3, 200), 2)
   24.2
   >>> round(powers_1 (5, 100), 2)
   10.33
   >>> round(powers_1 (7, 1000), 2)
   100.0
   

   Note

   More tests are provided in file powers-1.txt

2. Write the function powers_2() that takes two positive integers, x and maxn, and another integer, d, such that 0<=d<10, and returns the first number of the sequence of powers of x less than or equal to maxn such that its digit in the units position is d. If there is no such number, this function must return -1. Examples:

   >>> powers_2 (2, 100, 6)
   16
   >>> powers_2 (2, 100, 5)
   -1
   >>> powers_2 (5, 100, 5)
   5
   >>> powers_2 (5, 100, 3)
   -1
   >>> powers_2 (7, 1000, 3)
   343
   

   Note

   More tests are provided in file powers-2.txt

Solution

A solution is provided in file powers.py