Approximation to lnx

Question

A good approximation to ln_x  is given by 

 

(((3A²)/((5)+1))(A²)/(3)+1)*2A

 

Where A=(x-1)/(x+1) and 1/2≤x≤3/2

Use this formula to calculate ln0.7

Answer 1

Amy,

 

First find A for x = 0.7

 

A = (0.7-1)/(0.7+1) = -0.176

 

Now substitute for A in the first equation to get your answer.