Logarithm Approximation for Small Values of ‘x’

Swapnil Paliwal

doi:https://doi.org/10.14445/22315373/IJMTT-V16P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 16 | Number 2 | Year 2014 | Article Id. IJMTT-V16P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V16P511

Logarithm Approximation for Small Values of ‘x’

Swapnil Paliwal

Citation :

Swapnil Paliwal, "Logarithm Approximation for Small Values of ‘x’," International Journal of Mathematics Trends and Technology (IJMTT), vol. 16, no. 2, pp. 70-73, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V16P511

Abstract

In this paper, an approximation formula for logarithm( log10(1+x), log10(1-x) and log10(x) ) is introduced. These formulas give close approximation to the actual logarithm value. The equation for log10(1+x) and log10(1-x) will give close approximation only when the input i.e x ∈ [-1,1] and for log10(x) will give close approximation only when x ∈ [0,2] . Certain examples have been presented in this paper, while at the same time comparison with actual logarithm value is also made. Graphical representation of logarithm and my equation is also provided

Keywords

Logarithm Approximation for small values, Logarithm, Representation of Logarithm Algebraically, Logarithm Approximation For log10(1+x), log10(1-x) and log10(x) .

References

[1] Logarithm Wikipedia website [Online]. Available: http://en.wikipedia.org/wiki/Logarithm
[2] Padé Approximation website [Online]. Available: http://www.nezumi.demon.co.uk/consult/logx.htm
[3] SWAPNIL PALIWAL “Logarithm Approximation” in International Journal Of Mathematics, vol. 16 number 1, p. 12-14, Dec. 2014
[4] Tylor series Wikipedia website [Online].Available: http://en.wikipedia.org/wiki/Taylor_series
[5] Approximation for log function website [Online].Available: http://planetmath.org/approximationofthelogfunction