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).
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 ...
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.
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?
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...
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...
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?
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.
