This document discusses using the modified secant method to find the root of the function f(x) = ln(2) - 2*ln(x). It provides the initial value of x0 = 3 and time step of δ = 0.0001. The method is implemented in a ModifiedSecantMethod function, which iteratively calculates new values of x until the difference between iterations is less than 10-10. The result, x_Numerical, converges to approximately 1.4142135624.

1. xxx...
= 2
We need to find root of f (x)  ln(2)  2ln(x)
Find Root from Modified Secant Method
1) Initial x x0  3
2) Time steps δ  0.0001
ModifiedSecantMethod(δx0) i  0
x0  x0
ε0  100
εi 10 10  while 
xi1 xi
f xiδxi
f xi δ xi      f xi


 
εi1
xi1  xi
xi1
 100
i  i  1
x
ε



x_Numerical ModifiedSecantMethod(δx0)0 
x_Numerical
3
0.7437711009
1.2217389913
1.400486319
1.4141474062
1.4142135641
1.4142135624
1.4142135624




2. h(x_Numericaly_Numerical) 