The subject of logarithm encompasses a wide range of important elements. What is the point of logarithms? (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division. Natural log of a negative number - Mathematics Stack Exchange.
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 with negative bases for real numbers. Moreover, 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. 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). Calculate logarithms by hand - Mathematics Stack Exchange. 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... Furthermore, what algorithm is used by computers to calculate logarithms?. 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... From another angle, taylor Series for $\log (x)$ - Mathematics Stack Exchange. 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?
How do I square a logarithm? - Mathematics Stack Exchange. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful.
What's reputation and how do I get it? Instead, you can save this post to reference later. How is $\\ln$ pronounced by English speakers?.
📝 Summary
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