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 ...
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...
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).
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 ...
Does anyone know a closed form expression for the Taylor series of the function $f (x) = \log (x)$ where $\log (x)$ denotes the natural logarithm function?
I'm thinking of making a table of logarithms ranging from 100-999 with 5 significant digits. By pen and paper that is. I'm doing this old school. What first came to mind was to use $\\log(ab) = \\lo...
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 ...
What happens to the units of a physical quantity after I take its (natural) logarithm. Suppose I am working with some measured data and the units are Volts. Then I want to plot the time series on a log-scale, only the ordinate is on the log scale, not the abscissa.
