Given a positive number x, the task is to find the natural log (ln) and log to the base 10 (log10) of this number with the help of expansion.
Input: x = 5 Output: ln 5.000 = 1.609 log10 5.000 = 0.699 Input: x = 10 Output: ln 10.000 = 2.303 log10 10.000 = 1.000
- The expansion of natural logarithm of x (ln x) is:
- Therefore this series can be summed up as:
- Hence a function can be made to evaluate the nth term of the sequence for 1 ≤ x ≤ n
- Now to calculate log10 x, below formula can be used:
Below is the implementation of the above approach:
ln 5.000 = 1.609 log10 5.000 = 0.699
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Program to calculate the value of sin(x) and cos(x) using Expansion
- Middle term in the binomial expansion series
- Program to print binomial expansion series
- Sum of the Tan(x) expansion upto N terms
- Sum of N terms in the expansion of Arcsin(x)
- Find subsequences with maximum Bitwise AND and Bitwise OR
- Find the radii of the circles which are lined in a row, and distance between the centers of first and last circle is given
- Find the side of the squares which are lined in a row, and distance between the centers of first and last square is given
- Find minimum possible values of A, B and C when two of the (A + B), (A + C) and (B + C) are given
- Find the number of words of X vowels and Y consonants that can be formed from M vowels and N consonants
- Find smallest positive number Y such that Bitwise AND of X and Y is Zero
- Find two integers A and B such that A ^ N = A + N and B ^ N = B + N
- Find a number X such that (X XOR A) is minimum and the count of set bits in X and B are equal
- Program to find if two numbers and their AM and HM are present in an array using STL
- Find a number M < N such that difference between their XOR and AND is maximum
- Find the largest multiple of 2, 3 and 5
- Find n'th number in a number system with only 3 and 4
- Find smallest values of x and y such that ax - by = 0
- Find the Largest number with given number of digits and sum of digits
- Find the minimum value of m that satisfies ax + by = m and all values after m also satisfy
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.