Saturday, March 7, 2020

Approximations for Common Logarithm Function

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

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