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 superficially different, …

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 $\theta$, as long as the …

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 there a formu...

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 doesn't seem all that …

5 days ago · Here $y=\log_6 3\in (0,1)$, so for $1<5<6$ we have $\log_5 y<\log_6 y$. Hence $\log_5 (\log_6 3)<\log_6 (\log_6 3)$, so the second inequality in your chain is reversed.

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 $\log (1+x)$.

May 23, 2019 · Log base 4 (7) can be evaluated using the change of base formula. This can similarly be expressed as ln7 divided by ln4, using the natural logarithm. Using the above example, Why is it that …

Dec 5, 2023 · Since the default base of log can vary between and even within fields, seems a good rule of thumb is to treat ln as loge (of course), and log as unknown (re: base-2/10/e/whatever) until you …

What is the difference in this question between $\log$ and $\lg$? Ask Question Asked 9 years, 7 months ago Modified 1 year, 7 months ago

In mathematics, $\log n$ is most often taken to be the natural logarithm. The notation $\ln (x)$ not seen frequently past multivariable calculus, since the logarithm base $10$ finds relatively little use.