Details of logarithmic calculations?

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SUMMARY

This discussion focuses on the methods of calculating logarithmic values, specifically how \log{2} is determined to be 0.3010. Participants mention the use of Taylor's Series as a mathematical approach to approximate logarithmic values, particularly for inputs between 0 and 2. The conversation highlights the importance of understanding the underlying principles of logarithmic calculations and the convergence properties of infinite series.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with Taylor's Series and its application in calculus
  • Basic knowledge of limits and convergence in mathematical series
  • Ability to perform calculations involving natural logarithms (ln)
NEXT STEPS
  • Study the derivation and application of Taylor's Series for logarithmic functions
  • Explore numerical methods for calculating logarithms, such as Newton's method
  • Learn about the properties and applications of natural logarithms (ln) in various fields
  • Investigate the convergence rates of infinite series and their implications in calculus
USEFUL FOR

Mathematicians, students studying calculus, educators teaching logarithmic functions, and anyone interested in the mathematical foundations of logarithmic calculations.

kiru
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From where I can get the details of lograthmic calculations?How the values are found?and on what basis?
 
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Do you want to know for instance how \log{3} is found? That kind of calculation?
 
Jameson said:
Do you want to know for instance how \log{3} is found? That kind of calculation?
Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?
 
kiru said:
Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?

I would have the same question + how cosines are calculated.
 
There are a variety of ways.

The simplest is to use "Taylor's Series". It can be shown, in Calculus, that for x between 0 and 2, ln(x)= (x-1)- (1/2)(x-1)2+ (1/3)(x-1)3-...- ((-1)n/n)(x-1)n+... That infinite series does not converge very fast but it will give close to the correct value eventually.
 

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