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?

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 { …

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 16, 2012 · The units remain the same, you are just scaling the axes. As an analogy, plotting a quantity on a polar chart doesn't change the quantities, it just 'warps' the display in some useful way. …

Apr 5, 2017 · I've never encountered the following type of logarithmic simultaneous equations. I'm supposed to solve for x and y, but I just can't seem to figure it out. $$ \log_9 { (xy)} = \frac {5} {2}$$ …

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.

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.