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 …

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 …

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 $\\log(25)$?

May 13, 2016 · We can't really simplify the expression $ (\log_b a)^2$ since there exist no useful identities for powers of logarithms. Recall that, in some sense, logarithms themselves are …

Jun 28, 2017 · I have always heard an expression like $\\ln (x^2)$ pronounced aloud as "ell-enn ex squared". That is, the name of the function $\\ln$ is read aloud as a two-letter abbreviation. …

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

Mar 17, 2019 · When I have this equation: $\\ln(x+2) = \\ln(x^2)$, why can I just remove the $\\ln$ from both sides by raising it to the power of e. Does this not permanently change what the …

Mar 22, 2014 · Logarithms of different bases are related: they are simple multiples of each other. Common logarithms are $\log_ {10}$ (the base is usually skipped), and the natural logarithm …