Nov 26, 2021 · This is simply $\log (6)=\log (2\cdot 3)=\log (2)+\log (3)=\log (1)+\log (2)+\log (3)$. So there is only the functional equation "going on under the hood".

Nov 5, 2013 · Writing expression in terms of $\ln2$ and $\ln3$ Ask Question Asked 12 years, 1 month ago Modified 12 years, 1 month ago

Oct 14, 2023 · I was trying to figure out if $\\ln(3)/\\ln(2)$ is transcendental, when I found this post by b_jonas But there's a proof just as simple showing that $\\log 3/\\log 2$ is irrational. Suppose on …

Nov 30, 2013 · Does this limit: $$\\lim_{n\\to\\infty}\\ln(1+\\ln(2+\\ln(3+...+\\ln(n)))...)$$ exist ? And if yes, which value does it have ?

Aug 22, 2017 · Nevertheless, since the $86$ in the decimal expansion of $\ln3$ still reminded me of $6/7,$ but I already knew now that multiplication by $7$ is not a choice, I tried seeing it as $5/6$ or …

Jun 22, 2023 · The Lambert-W function can only be computed numerically. It solves the equation $ye^y=x$. If you want to solve such equations by hand (to be more precise , only with ...

Mar 23, 2020 · If you plug \begin {eqnarray*} x=\left (\dfrac {2^ {\ln 2}} {3^ {\ln 3}}\right)^ {\frac {\ln2} {\ln^23-\ln^22}} \end {eqnarray*} into your casio (other brands of calculator are avaiable) ... you do …

Oct 26, 2015 · If $3^x = 3^{x\\log _3\\left(3\\right)}$ then the derivative of $3^x$ is $\\log_3\\left(3\\right) \\cdot 3^x$, by the product and chain rules; which is really just $3^x$. This is not the 'right' answer t...

Mar 7, 2015 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …

Mar 4, 2019 · Our teacher tells us to convert it this way $ 3^x = e^ {\ln 3^x}= e^ {x\cdot\ln 3}$ and then use the rule $e^u\cdot u'$ but I can't understand where $\ln$ comes from ...