CSC $222$ Module $4$ Coding Assignment $-$ Recursion

Write a program that uses a recursive call to find the integer logk of a number. Where logk$,$ returns the integer log of a number in a designated base. For example, the integer base $10log$ of $1234$ is $3,$ and the integer base $2log$ of $1234$ is $10.$ This is a relatively easy calculation. You simply repeatedly divide the number by the base using integer division until the quotient is less than the base and count the number of completed divisions.

$\frac{1234}{10}=123(1)$

$\frac{123}{10}=12(2)$

$\frac{12}{10}=1(3)$

$\frac{1234}{2}=617(1)$

$\frac{617}{2}=308(2)$

$\frac{308}{2}=154(3)$

$\frac{154}{2}=77(4)$

$\frac{77}{2}=38(5)$

$\frac{38}{2}=19(6)$

$\frac{19}{2}=9(7)$

$\frac{9}{2}=4(8)$

$\frac{4}{2}=2(9)$

$\frac{2}{2}=1(10)$

Notice that the number $1234$ is actually $1{10}^3+2{10}^2+3{10}^1+4{10}^0$ and in base $2$ the number $1234$ would be $12^{10}+02^9+02^8+12^7+12^6+02^5+12^4+02^3+02^2+12^1+02^0$

The key point here is that the highest power in these numbers in the integer log value.

Hint use the number and the base as arguments to your recursive call, then your base case is when number is less than base and returns $0,$ and the general case returns $1$ plus the returned value of the recursive call.

Your program should behave as follows.

Please enter a number to find the integer log of $1234$

Please enter the base for the calculation

$2$

The base $2$ integer log of $1234$ is $10$

Would you like to enter another pair of numbers?

Please enter $"$ y $"$ for yes or $"$ n $"$ for no$.$

b

Please enter $"$ y $"$ for yes or $"$ n $"$ for no$.$

y

Please enter a number to find the integer log of

$1$

$1234$

Please enter the base for the calculation

$5$

The base $5$ integer log of $1234$ is $4$

Would you like to enter another pair of numbers?

Please enter $"$ y $"$ for yes or $"$ n $"$ for no$.$

n

Good$-$bye!

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