I have a problem that is very simple in concept but very difficult to actually solve.

I need to find the best fit polynomial of degree at most 4 for f(x)=ln(x) on the interval [1,4].

So far I have gotten to the point where I need to solve the system of equations: $0=-3a\_0-\frac{15a\_1}{2}-21a\_2-\frac{255a\_3}{4}-\frac{1023a\_4}{5}-3+ln\left(256\right),\\0=-\frac{15a\_0}{2}-21a\_1-\frac{255a\_2}{4}-\frac{1023a\_3}{5}-\frac{1365a\_4}{2}-\frac{15}{4}+8ln\left(4\right),\\0=-21a\_0-\frac{255a\_1}{4}-\frac{1023a\_2}{5}-\frac{1365a\_3}{2}-\frac{16383a\_4}{7}-7+\frac{64}{9}ln\left(64\right),\\0=-\frac{255a\_0}{4}-\frac{1023a\_1}{5}-\frac{1365a\_2}{2}-\frac{16383a\_3}{7}-\frac{65535a\_4}{8}-\frac{255}{16}+64ln\left(4\right),\\0=-\frac{1023a\_0}{5}-\frac{1365a\_1}{2}-\frac{16383a\_2}{7}-\frac{65535a\_3}{8}-29127a\_4-\frac{1023}{25}+\frac{1024ln\left(4\right)}{5}$

I know how to do this in theory, but the execution is incredibly tedious and errors easily find their way in. I was wondering if anyone knew a good system of equation calculator, symbolab seems to only be able to solve up to 4 terms, or code for solving a 5 term system of equations on matlab.