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 $\\log(25)$?

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?

Apr 30, 2016 · I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\\log x·\\log 2x < 0$$ How would one solve this? And if it weren't possible, what would its …

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 …

Jun 2, 2022 · Explore related questions logarithms graphing-functions See similar questions with these tags.

Jan 9, 2017 · For example, the following "proof" can be obtained if you're sloppy: \begin {align} e^ {\pi i} = -1 & \implies (e^ {\pi i})^2 = (-1)^2 & \text { (square both sides)}\\ & \implies e^ {2\pi i} = 1 & \text { …

Nov 8, 2013 · "exponential decay" describes things that have a half-life and is a very common term. I'm not sure what "logarithmic decay" means, if anything.

Aug 19, 2013 · I have a very simple question. I am confused about the interpretation of log differences. Here a simple example: $$\\log(2)-\\log(1)=.3010$$ With my present understanding, I would interpret …

Problem $\\dfrac{\\log125}{\\log25} = 1.5$ From my understanding, if two logs have the same base in a division, then the constants can simply be divided i.e $125/25 = 5$ to result in ${\\log5} = 1.5$...

Nov 21, 2019 · This just depends on how the author decides to define the $\log$ function. Most authors leave $\log (0)$ undefined. You could define $\log (0)$ to be $-\infty$, but it's unclear that this is helpful.