My teacher told me that the natural logarithm of a negative number does not exist, but $$\ln (-1)=\ln (e^ {i\pi})=i\pi$$ So, is it logical to have the natural logarithm of a negative number?
Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest). Historically, they were also useful because of the fact that the logarithm of a product is the sum of the ...
The point is: the complex logarithm is not a function, but what we call a multivalued function. To turn it into a proper function, we must restrict what $\theta$ is allowed to be, for example $\theta \in (-\pi,\pi]$. This is called the principal complex logarithm and is usually denoted by $\operatorname {Log}$ (capital L).
Thank you for the answer. I am aware of the general solutions for complex numbers. In my question above I am specifically asking to the definition for real numbers. It is in that scenario that I have always only understood logarithms as defined for positive numbers, although there seems to be solutions for negative bases. My apologies if that wasn't clear.
I can raise 0 0 to the power of one, and I would get 0 0. Also −1 1 to the power of 3 3 would give me −1 1. I think only some logarithms (e.g log to the base 10 10) aren't defined for 0 0 and negative numbers, is that right? I'm confused because on all the websites I've seen they say "logs are not defined for 0 0 and negative number". On one website it says " logb(0) log b (0) is not ...
Shortly after the work of Napier, Briggs, inspired by that work, produced tables of the base $10$ logarithm. Related tables were used for computations for centuries.
The discrete Logarithm is just reversing this question, just like we did with real numbers - but this time, with objects that aren't necessarily numbers. For example, if $ {a\cdot a = a^2 = b}$, then we can say for example $ {\log_ {a} (b)=2}$.
I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that logarithms are calculated directl...
Here I was exposed to so many variations: Saying the two letters l n Saying "log"/"logarithm" Saying "natural log" Saying "log e" All of the above were native-English speakers from different parts of the world. No one pronounced it like we Israelis do, as "lan". As for your "linn", I believe it was a New Zealander. Their e's sound like i's ...
I have read through questions like Calculate logarithms by hand and and a section of the Feynman Lecture series which talks about calculation of logarithms. I have recognized neither of them useful...
