Sep 11, 2020 · How to evaluate $$\log (i)?$$ Also, how to evaluate $$\log (3+4i)?$$ I am reading complex analysis and I know that logarithm is a multibranched function and is periodic.

Dec 4, 2020 · Hence, $$ \log_a (a^x) = x \text { and } a^ {\log_a {x}}=x $$ are both true by definition. The hardest part is trying to explain why these two conceptions of logarithms, while …

Jan 9, 2017 · This is called the principal complex logarithm and is usually denoted by $\operatorname {Log}$ (capital L). Technically, it doesn't matter to what range you restrict …

Dec 3, 2025 · You wrote $$\log_5 (\log_4 3) = \frac {\ln 3 - \ln 4} {\ln 5}, \quad \log_6 (\log_6 3) = \frac {\ln 3 - \ln 6} {\ln 6},$$ but actually $$\log_4 3 = \frac {\ln 3} {\ln 4} \quad\text {so}\quad \ln …

Yes one can deduce that $\log a \log b$ is also $\log (b^ {\log a})$. These equations are not mentioned much, perhaps because they can easily be deduced from the other laws (and it …

Jan 13, 2021 · If you accept (otherwise this can easily be proved) that $\log ()$ is a concave function, then it suffices to show (cf. Jensen) that $x$ is a tangent to $\log (1+x)$.

Apr 23, 2017 · I have seen people look at log (several digit number) and rattle off the first couple of digits. I can get the value for small values (aka the popular or easy to know roots), but is …

Aug 19, 2013 · 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 result as …

6 days ago · I am confused from the first equality, what do those expressions have to do with the function in question?

Oct 11, 2015 · How to derive the value of $\log (-1)$? Ask Question Asked 10 years, 1 month ago Modified 10 years, 1 month ago