ln ( x ) ≈ a x 1 / a − a , which...
, which is good for large value of . Where does it come from?
Answer & Explanation
For large we have
(by Taylor's theorem) which gives
so the approximation is accurate once is large relative to . By the way, I would describe this in exactly the opposite way: that is a good approximation to ! It's not as if is particularly easy to compute for large .
This is the same thing as asserting that, if and a is very small, then
which is true, since
in other words, the derivative at of is .