Need Aproximate expressions for : ln(x) and 1/ln(x) Thanks

In summary, the approximate expression for ln(x) is x - 1 when x is close to 1, while the approximate expression for 1/ln(x) is 1/(x - 1) when x is close to 1. To find these approximations, you can use the Taylor series expansion for ln(x) at x = 1. However, these approximations are only valid for values of x close to 1, as their accuracy decreases as x gets further away from 1. Approximate expressions for ln(x) and 1/ln(x) can be useful in simplifying complex expressions and providing rough estimates without having to use a calculator or perform more complex mathematical operations.
  • #1
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Hi there:
I am looking for approximate expressions for the two functions: ln(x) and 1/ln(x) . Any help?
Thanks in advance.
 
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  • #2
Approximations where, for what? Did you try Taylor expansions?
 
  • #3
ln(x) is not analytic at x=0. You need to use a series around some other value. If you use the series for ln((1+x)/(1-x)) you will able to get a series for any y=(1+x)/(1-x) for -1<x<1.
 

1. What is the approximate expression for ln(x)?

The approximate expression for ln(x) is x - 1 when x is close to 1.

2. What is the approximate expression for 1/ln(x)?

The approximate expression for 1/ln(x) is 1/(x - 1) when x is close to 1.

3. How do you find an approximate expression for ln(x)?

To find an approximate expression for ln(x), you can use the Taylor series expansion for ln(x) at x = 1, which is ln(x) = (x - 1) - (x - 1)^2/2 + (x - 1)^3/3 - ...

4. Can an approximate expression for ln(x) be used for any value of x?

No, an approximate expression for ln(x) is only valid for values of x close to 1. As x gets further away from 1, the accuracy of the approximation decreases.

5. Why do we need approximate expressions for ln(x) and 1/ln(x)?

Approximate expressions for ln(x) and 1/ln(x) can be useful when doing calculations or analyzing data, as they can simplify complex expressions and make them easier to work with. They can also give a rough estimate of the value of ln(x) or 1/ln(x) without having to use a calculator or perform more complex mathematical operations.

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