Aug 15, 2015 · The logarithm is an isomorphism between the vector space of positive-real numbers to the vector space of real numbers. And as every isomorphism is a linear function, so is the logarithm.

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 number?

Feb 25, 2014 · Why must the base of a logarithm be a positive real number not equal to 1? Ask Question Asked 12 years, 1 month ago Modified 6 years, 5 months ago

Oct 11, 2020 · Why does the inequality sign change when applying a logarithm on both sides, with the base less than $1$? I came across the following math which I solved if 2 ways, $$ \left (\frac {1} …

Oct 20, 2021 · I found the following rule while reviewing logarithms: "Raising the logarithm of a number by its base equals the number.", i.e., $$ b^ {\log_b (k)} =k.$$ Why is this true?

Aug 10, 2020 · Until we make the generalization of exponents to arbitrary powers, there is no hope of describing the inverse logarithm as an exponential function. One "convenience" of the antilog …

Jul 5, 2020 · The discrete Logarithm is just reversing this question, just like we did with real numbers - but this time, with objects that aren't necessarily numbers. For example, if $ {a\cdot a = a^2 = b}$, …

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 …

I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that logarithms are calculated directl...

Dec 5, 2023 · Beware that $\log$ does not unambiguously mean the base-10 logarithm, but rather "the logarithm that we usually use". In many areas of higher mathematics, $\log$ means the natural …