Jan 10, 2021 · 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 …

Jan 9, 2017 · 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 …

May 7, 2015 · How do I square a logarithm? Ask Question Asked 10 years, 7 months ago Modified 2 years, 5 months ago

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...

Jun 28, 2017 · 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 …

You can define everything you want, but will this newborn object satisfy properties you want, depends on your definition. Assume, we do have logarithms for negative numbers and zero and all the properties …

Nov 29, 2013 · 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?

Oct 29, 2021 · 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 …

Dec 27, 2016 · I had "the logarithm of a number is the index to which the base is raised to equal that number" drilled into me 60 years ago. It's still helpful when I need a reminder what does what. In this …