Chapter 5, Problem 13E

Program Plan Intro

Recursive method:

• A method calls itself is as recursive method.
• In recursive function base case will stop recursion and return value instead of calling function.

Program to implement:

1. a. Recursive functions for John Napier’s Method to print logarithms.
2. b. Modified recursive function to find logarithm of a specific number between “100” and “1000”.
3. c. Function to call above function to find logarithm of a number not between “100” and “1000”.

Explanation of Solution

//b. Modified recursive function to find logarithm of a number between 100 and 1000:

//Recursive function to find logarithms of a number between 100 and 1000

void logarithmOf(double first, double second, double firstLog, double secondLog,double num)

{

//If difference between adjacent numbers is greater than tolerance

if (fabs(first - second) > tolerance)

//If number is less than square root of (first*second)

if (num < sqrt(first*second))

//Function calls itself recursively with parameters first,sqrt(first*second),firstLog,(firstLog+secondLog)/2 and num

logarithmOf(first,sqrt(first*second),firstLog,(firstLog+secondLog)/2,num);

//If number is greater than or equal to square root of (first*second)

  else

//Function calls itself recursively with parameters sqrt(first*second),second,(firstLog+secondLog)/2,secondLog and num

logarithmOf(sqrt(first*second),second,(firstLog+secondLog)/2,secondLog,num);

//If difference between adjacent numbers is less than or equal to tolerance

else

//Print logarithm of number

cout << "log(" << num << ") = " << firstLog <�...

Explanation of Solution

//c. Function to call modified function to find logarithm of a number not between 100 and 1000:

//Function to find logarithm of number does not between 100 and 1000

void newlogarithm(double first, double second, double firstLog, double secondLog,double num)

{

  //If number is less than 10^2 and greater than 10^3

  if (num < pow(10.0,2) || num > pow(10.0,3))

  //Call function  logarithmOf()

logarithmOf(first, second, firstLog, secondLog,num);

  //If number is between 100 and 1000

  else

  //Print error message

  cout<<"Input is invalid"<<endl;

}

//Program begins with main() function

int main()

{

  //Declare variable

  int num;

  //Call recursive function logarithm()

  cout<<"Result of function logarithm(): "<<endl;

  logarithm(2,6,0.3010,0.778);

  //Prompt and read number from user

  cout<<"Enter number between 100 and 1000: "<<endl;

  cin>>num;

  //If number is between 100 and 1000

  if(num>100 && num<1000...