Steinharts-Hart equation: Calculating the coefficients marathon

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The discussion centers on calculating the coefficients of the extended Steinhart-Hart equation for an NTC thermistor using temperature-resistance pairs. The user initially struggled with the calculations and sought verification of their substitutions and methodology. After some confusion with numerical inputs, they discovered that their equations were correct, but incorrect values were entered into their calculator. Ultimately, they successfully implemented the equations in C programming, which yielded accurate results. This highlights the importance of careful data entry in mathematical calculations.
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Homework Statement
I would like to calculate coefficients for the Steinharts-Hart equation but it is alarge system...
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Steinharts-Hart equation
I read about the Steinharts-Hart's equation here and I decided to try and calculate the four coefficients of the extended Steinharts-Hart's equation:

$$\frac{1}{T} = A + B \ln(R) + C \cdot (\ln(R))^2 + D\cdot (\ln(R))^3 $$

Where T is a temperature and R is a resistance of the e.g. NTC thermistor. On the supplied website it is written that:

Sometimes calculation of coefficients is done using special temperature values. Inserting four value pairs in the range of interest into the extended Steinhart-Hart poylonm leads to a system of linear algebraic equations (Three value pairs for the standard Steinhart-Hart polynom). Temperatures typically used are for example 0° C, 15° C, 25° C and 70° C. By solving this system the values for A, B, C and D can be determined.

Well I have chosen my NTC thermistor, found the documentation and took four of the temperature - resistance pairs. Then I tried to calculate the first coefficient, but it is a marathon (attachment)!

I would need someone to quick check for errors. I am not sure my substitutions were made corectly... Do you think I am even on the right track?
 

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At this point I managed to calculate all the coefficients, but probably they are wrong. Here is the entire calculation. If anyone spots any errors please let me know.
 

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As it turned out. Al lthe equations were correct, but I inputed the wrong numerical values in my calculator. At the end I inserted equatioins in C programming language and it calculated everything perfectly.
 
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