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 …

Nov 21, 2019 · 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 …

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 …

Aug 14, 2020 · 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 $\\log(25)$?

Jan 10, 2021 · 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 …

Jan 9, 2017 · 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} = …

Oct 26, 2021 · That is indeed much more complex than I thought, I will come back to this and try once I get to complex number and calculus, which is probably a year later. But at least now I …

Jun 2, 2022 · Explore related questions logarithms graphing-functions See similar questions with these tags.

Nov 29, 2013 · 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?

I do not understand how $\\log_2(x) + \\log_4(x) = \\log_2({x^{3/2}})$ Where does $^{3/2}$ come from? Naming the rules and steps would be helpful.