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- What is the point of logarithms? How are they used? [closed]
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 population to double or for a bank balance to reach a given value with compound interest) Historically, they were also useful because of the fact that the logarithm of a product is the sum of the
- 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 ${\\log5} = 1 5$
- 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?
- 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 - 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 - 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 $\\log(25)$?
- 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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