Hi, if you approximate your function by series expansion of a high order, the zero of this polynomial can be used as an initial guess of the zero of your original function. Nevertheless, finding the zero of a high order polynomial requires the use of a numerical method. So there is no benefit compared to a numerical solution of the original function no?

Hello

Can I use lnx~(1-x) for finding roots of

x+.868 ln(.0006275x+.0052)=0

Thanks

Hi, the problem is that ln(x) can be approximated at the first order by (x-1) if x is close to one only. In your case, the zero of your equation is xsol = 4.208425... leading to 0.0006275*xsol+0.0052 = 0.00784078 that is close to zero.

Hello

Solve this equation easily

series expansion techniques can be useful in solving non linear equations.

I agree with Richard Epenoy and Piyapong Buahom. The equation is easily solved using simple iteration and iterates would converge to exact solutions in a relatively few steps. The need to pursue series approximations to the logarithmic function to solve the problem is only an academic exercise. Moreover, Richard Epenoy has explained lucidly the impossibility of getting good answers with linear approximation of the logarithmic function. Nonlinear approximations yield algebraically complicated equations to solve which in itself is an approximation of the posed problem.

Exact solution is possible for the problem.