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 …

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 ${\\log5} = 1.5$...

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 the resul...

Jan 9, 2017 · 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 …

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 $\\log(25)$?

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. …

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?

Nov 8, 2013 · I am a little unclear on whether they are distinctly different or whether this is a 'square is a rectangle, but rectangle is not necessarily a square' type of relationship.

Mar 21, 2016 · Close to $0$ a logarithm diverges to $-\infty$... How close to zero do you need to go? A fast (and quite rough) approximation is a decimal logarithm is minus a number of zeros in front of …

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.