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Eintrag vom: 09.04.2013.

0 This question already has answers here: Proof of the power rule for logarithms (6 answers)

 

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).

 

I want start by saying that my math skills aren't great and I'm trying to learn. I took a look at square root. Squaring the number means x^2. And if I understood the square root correctly it doe...

 

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.

 

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 ...

 

Does anyone know a closed form expression for the Taylor series of the function $f(x) = \\log(x)$ where $\\log(x)$ denotes the natural logarithm function?

 

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?

 

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...

 

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

 

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