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Is there a way to compute a #ln# or a #log# function without a calculator? (an approximation). Say #ln2# or # ln3#

Answer 1

Yes, there are methods to approximate the natural logarithm (ln) or logarithm (log) functions without a calculator. One common approach is to use Taylor series expansions, specifically the Maclaurin series for ln(1 + x), where x is close to 0. For ln(2) or ln(3), you can use properties of logarithms to express them as ln(2) = ln(2/1) and ln(3) = ln(3/2) + ln(2), then approximate ln(2/1) and ln(3/2) using the Taylor series. Alternatively, you can use iterative methods such as the Newton-Raphson method or binary search algorithm to approximate ln(2) or ln(3). These methods require some computational steps but can provide reasonably accurate approximations without a calculator.

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Answer 2

Julia Adams

There are natural log tables online. Here's one:

https://tutor.hix.ai

I'm not sure if this is still the case, but these used to be in the index of textbooks.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.