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 ${\\log5} = 1.5$...
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'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. $$ \log_9 { (xy)} = \frac {5} {2}$$ $$ \lo...
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.
