Log of a negative number - Mathematics Stack Exchange
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 θ θ is allowed to be, for example θ ∈ …
What is the point of logarithms? How are they used?
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 …
Why can the base of a logarithm not be negative? [duplicate]
Sep 27, 2021 · The long story short is that "logarithm" isn't a function on the complex plane (because one input can map to multiple outputs), and there's rarely a real answer when dealing with negative …
Complex logarithm base 1 - Mathematics Stack Exchange
Nov 30, 2025 · A logarithm to the base + 1 seems difficult to define because of that issue with division by zero on one logarithmic branch. We can consider a limited definition for base − 1 and argument of …
Why must the base of a logarithm be a positive real number not equal …
Feb 25, 2014 · This logarithm would be the inverse of the function y = (− 4)x, which can only be evaluated for exponents that can be written as a fraction where the denominator is odd. Remember a …
Easy way to compute logarithms without a calculator?
Feb 14, 2016 · The definition of a logarithm in reals may help: logb a log b a is such a real number c c that satisfies bc = a b c = a. For example, log2 131072 = 17 log 2 131072 = 17 because 217 = …
terminology - What gives the natural logarithm its name? What's ...
Mar 4, 2021 · I know that the natural logarithm is defined as ln(x) ln (x) or loge(x) log e (x), where e e is the Euler number. But what is so "natural" about it? Is there an explanation on why that name was …
How to convert a logarithm from base 10 to base 2?
Jul 4, 2023 · How to convert the base $10$ logarithm to base $2$? The question didn't provide the value of the logarithm. The question is: "Given a logarithm in base 10, how can you use the change …
Isn't square root a bit like Log()? - Mathematics Stack Exchange
May 26, 2020 · the inverse of x2 x 2 is a the square root, the inverse of 2x 2 x is the (base 2) logarithm. The inverse of xa x a is the a a -th root, the inverse of ax a x is the (base a) logarithm.
What is the best way to calculate log without a calculator?
Aug 14, 2020 · As the title states, I need to be able to calculate logs (base $10$) on paper without a calculator. For example, how would I calculate $\\log(25)$?