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