Design and write a C program that approximates the value of ln(x) for inputted values of x and n,

Question

The value of ln(), for 0 < < 2, can be calculated using ln(1 + ) = (x-1/1) - (x-1)²/2 + (x-1)³/3 + ⋯. This value can be approximated using the first n terms ln(x) ≈

Answer 1

Hi Deji! Here is my proposal for this, which seems to work well for me :-)

#include <math.h>

#include <stdio.h>

#include <stdlib.h>

double ln_approx(double x, int n) {

double accumulator = 0;

// The Taylor series is in terms of "x+1".

x = x - 1;

for (int i = 1; i <= n; i++) {

const int multiplier = i % 2 == 0 ? -1 : 1;

accumulator += multiplier * pow(x, i) / i;

}

return accumulator;

}

int main(int argc, char** argv) {

const double x = atof(argv[1]);

const int n = atoi(argv[2]);

const double result = ln_approx(x, n);

printf("ln(%f) ~= %f (%i iterations)\n", x, result, n);

}