Approximations for Common Logarithm Function
A Personal Note:
Hi, everyone! I had heart surgery two weeks ago, and I am still in recovery. However, things are going well and I am breathing a lot easier. Glad to be back.
- Eddie
Transformations
I am trying to find an approximation polynomial for the common logarithmic function, log(x). My goal is to find an approximation polynomial which is accurate to at least 2 decimal points.
The first fit was to fit x against log(x). However, if I apply a transformation, then compare data, I was able to get better results.
I used a TI-84 Plus CE to fit a quadratic and cubic polynomial to data generated by the following sets:
x, log(x)
x, log(x^(1/2))
x, log(x^(1/3))
x, log(x^(1/4))
Comparison of Approximations
The table compares two approximations against the logarithmic function.
POLY 1:
log x ≈ -.63965*t^2 + 3.06651*t - 2.44635
POLY 2:
log x ≈ .39510*t^3 - 2.10974*t^2 + 4.805*t - 3.091
In both polynomials, t = x^(1/4)
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
A Personal Note:
Hi, everyone! I had heart surgery two weeks ago, and I am still in recovery. However, things are going well and I am breathing a lot easier. Glad to be back.
- Eddie
Transformations
I am trying to find an approximation polynomial for the common logarithmic function, log(x). My goal is to find an approximation polynomial which is accurate to at least 2 decimal points.
The first fit was to fit x against log(x). However, if I apply a transformation, then compare data, I was able to get better results.
I used a TI-84 Plus CE to fit a quadratic and cubic polynomial to data generated by the following sets:
x, log(x)
x, log(x^(1/2))
x, log(x^(1/3))
x, log(x^(1/4))
Comparison of Approximations
The table compares two approximations against the logarithmic function.
POLY 1:
log x ≈ -.63965*t^2 + 3.06651*t - 2.44635
POLY 2:
log x ≈ .39510*t^3 - 2.10974*t^2 + 4.805*t - 3.091
In both polynomials, t = x^(1/4)
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
