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- logarithms - What is the best way to calculate log without a calculator . . .
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 $\\log(25)$?
- 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?
- Multiplying two logarithms (Solved) - Mathematics Stack Exchange
I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\\log x·\\log 2x lt; 0$$ How would one solve this? And if it weren't possible, what would its doma
- logarithms - Log of a negative number - Mathematics Stack Exchange
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 { (calculate the squares)}\\ \implies \log (e^ {2\pi i}) = \log (1) \text { (take the logarithm)}\\ \implies 2\pi i = 0 \text
- logarithms - What is the difference between logarithmic decay vs . . .
"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
- logarithms - Interpretation of log differences - Mathematics Stack Exchange
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
- logarithms - Dividing logs with same base - Mathematics Stack Exchange
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 ${\\log5} = 1 5$
- logarithms - Units of a log of a physical quantity - Mathematics Stack . . .
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 However, some quantities are 'naturally' expressed as logs (dB, for example), but these are always dimensional quantities (sometimes implicitly referenced to a known quantity)
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