Logarithms And Exponentials

In recent times, logarithms and exponentials has become increasingly relevant in various contexts. Multiplying two logarithms (Solved) - Mathematics Stack Exchange. I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\\log x·\\log 2x < 0$$ How would one solve this?

And if it weren't possible, what would its doma... It's important to note that, what is the point of logarithms? 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 ${\\log5} = 1.5$... logarithms - How to type logarithmic functions into Desmos graphing .... Explore related questions logarithms graphing-functions See similar questions with these tags. logarithms - Interpretation of log differences - Mathematics Stack Exchange. Another key aspect involves, 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... 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?

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 $\\log(25)$? Moreover, logarithms - Log of a negative number - Mathematics Stack Exchange.

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Instead, you can save this post to reference later. 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. From another angle, however, some quantities are 'naturally' expressed as logs (dB, for example), but these are always dimensional quantities (sometimes implicitly referenced to a known quantity).

logarithms - Why does a base of Log or exponential function have to be ....