$\log _{-3}\left( 9 \right)$?
Why aren't logarithms defined for negative $x$?
How can I import the configuration on a different site? I have this error when I try to import the config of an another site:     The staged configuration cannot be imported, because it originates   from a different site than this site. You can only synchronize   configuration between cloned instances of this site.   I have 10 customers, and I need to sync my site configuration with 10 different websites. The site UUID is a problem for sharing a configuration with a different website. Is there a solution? What are the regional Pokémon? I have heard that there are some Pokémon that are region specific.  Could someone please clarify which Pokémon are region specific and in which regions that they can be found in? Definitions of connected space I have seen several definitions of connected space, but I would like to discuss those from . I am concerned about these:  $X$ is disconnected, if it is the union of two disjoint nonempty open sets.  What about $[0,1] \cup [2,3] $ ? It is not the union of two disjoint nonempty open sets, so it is connected?  $X$ is connected, when it cannot be divided into two disjoint nonempty closed sets.  What about $(0,1) \cup (2,3) $ ? It cannot be divided into two disjoint nonempty closed sets, so it is connected?   Maybe I don't understand what "divided" means. During Order of the Phoenix, Voldemort tries his best to lure Harry to the Ministry so that Harry retrieves the prophecy for him. In the aftermath, while Harry follows Bellatrix towards the exit, he raises a valid question:  ”Why couldn’t he (Voldemort) come and get it (the prophecy) himself?”  This is a valid question, the prophecy is labeled as referring to the Dark Lord and maybe Harry Potter. Only those mentioned can retrieve the prophecy, so Voldemort should have been able to get it, assuming he is the Dark Lord of the prophecy. Bellatrix gives a good answer:  “Get it himself?” shrieked Bellatrix on a cackle of mad laughter. “The Dark Lord, walk into the Ministry of Magic, when they are so sweetly ignoring his return? The Dark Lord, reveal himself to the Aurors, when at the moment they are wasting their time on my dear cousin?”  Despite the cackle of mad laughter, the reasoning is sound, Voldemort didn't want to reveal himself. Yet he does exactly that when he appears in the Ministry and is seen by the Minister himself, and he exposes himself for no gain. Bellatrix may or may not have been able to escape without his help, but he couldn't know that before he came, and his other followers that were captured were freed again a few months later, so it wouldn't have mattered much, he would have freed her, too. So why did he go to the Ministry and reveal himself? What is the difference between can and could in 'Can/could you please explain this to me?' Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words? Adobe Illustrator: strange behavior while aligning objects I am creating icons with Adobe Illustrator during which process I use the Align tool quite frequently.  All of a sudden, the align tool started behaving quite strangely.  When I select two objects and specify that I want to align to a key object, when I press align it seems to only align halfway to where it should be.  When I press align again it aligns halfway again - after I press it several more times, it finally gets to where it needs to be.  Also, when I try to align to artboard, it pushes the object out to a seemingly random place.  Here is a video showing exactly what I mean:   What setting did I accidentally set to make align behave like this? How does new shield system work? Laravel loading error in Ubuntu 14.04 Primes congruent to 1 mod 6 I came across a claim that I found interesting, but can't seem to prove for some reason. I have the feeling it should be easy  a prime $p$ can be written in the form $p = a^2 -ab +b^2$ for some $a,b\in\mathbb{Z}$ if and only if $p\equiv 1\bmod{6}$ In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $dy = f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential). Then if we rearrange we get $dy/dx$ which could be seen as a ratio.   I wonder if the author says this because $dx$ is an independent variable, and $dy$ is a dependent variable, for $dy/dx$ to be a ratio both variables need to be independent.. maybe? When I want to register an account with Gmail now, it says "Google will send a text message containing a verification code to your mobile phone."  I don't want to give Google my mobile phone number!!  How do I get around this? How do I migrate an SVN repository with history to a new Git repository? How do I change a user name in Windows 7? Some webpages forces mobile version even I change user-agent. I changed user-agent in built-in browser and "Dolphin Browser HD",  I am checking it on page www.user-agent-string.info  Main problem is engadget.com, always in mobile version. I tried to clean cookies, restart browsers etc.  This is my results:   in built-in browser, user-agent - "desktop"   () doesn't work, redirects to mobile version   in "Dolphin Browser HD", user-agent - "desktop"    (NSFW: redtube.com) doesn't work, redirects to mobile version  (allegro.pl) works fine  in "Dolphin Browser HD", user-agent - "IPad"   () doesn't work, redirects to mobile version  (allegro.pl) works fine (NSFW: redtube.com) works fine  in "Dolphin Browser HD", user-agent - "custom": Mozilla/5.0 (Windows NT 6.0; rv:7.0.1) Gecko/20100101 Firefox/7.0.1   (engadget.com]) doesn't work, redirects to mobile version  (NSFW: redtube.com) doesn't work, redirects to mobile version  (allegro.pl) works fine    Maybe this pages using "adobe flash" user-agent detection ?  (I'am using Asus Transformer TF101, Android 3.2.1, Adobe Flash Player 11) Why use a z test rather than a t test with proportional data? When testing the difference between 2 proportions why do we use a z-test rather than a t-test?    Further, is there a simple way to conduct an omnibus test for significant differences between more than 2 proportions (in the form of percentages). Is there an equivalent to a one-way ANOVA for this?  I imagine that you could use logistic regression (assuming you have the original data for the proportions in the form of 0s and 1s) Are there other options? show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ Show that $\displaystyle\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ for all $k,l, n\geq 0$ with $k+l \leq n.$  The $k+l\leq n$ part doesn't seem that important. The claim clearly holds for $n=0,$ and in that case $k$ and $l$ must both be zero. I think the claim can be shown by induction, but I'm not sure how to do so; I'm not sure how to use the inductive hypothesis to prove the inductive step. The sum on the LHS is not always an integer, so finding a combinatorial argument doesn't seem very feasible. For $n = 1,$ we can have $(k,l) = (0,0), (1,0), (0,1),$ and in each case the sum holds. Perhaps multiplying both sides by a number (idk ${n-l\choose k}$) might be useful? Did Emperor Palpatine know about Luke and Leia from the beginning? Did Emperor Palpatine know that Padme had given birth to twins while it was happening?  Was it his long-term goal to have Vader only discover his offspring later, at some "correct" moment? If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$ I was working my way through some number theoretic proofs and being a newbie am stuck on this problem :     If $(x, 4) = 2$ and $(y, 4) =2$, then $(x + y, 4) = 4$,     where $(a,b)$ denotes the greatest common divisor of $a$ and $b$.   My Solution  (Incorrect)   $x-4 = 2t$ $y-4 = 2p$ $x + y - 8 = 2(t+p) \Rightarrow x + y - 4 = 2f + 4 = 2(f+2)\Rightarrow 2$ divides $(x+y , 4)$   My Question:  My solution is definitely inadequate. Can someone help me out? I am new to TeX/LaTeX. How do I install TeX on Windows (7)? It seems that there are many different implementations, so which one is best for my OS? I'm going to encrypt the characters Zhu, and decrypt them using RSA. I'm using the public key $\{e, n\}$ and private key $\{d, n\}$. The values of $e$, $d$ and $p$ I get from my textbook: $e = 17$, $d = 53$, $n = 77$.  It works fine when the number is smaller than 76, but in my example below, it doesn't work:  z = 90  h = 104  u = 107  e = 17 d = 53 n = 77  print z,h,u  c_z = z ** e % n c_h = h ** e % n c_u = u ** e % n  print c_z, c_h, c_u  p_z = c_z ** d % n p_h = c_h ** d % n p_u = c_u ** d % n  print p_z, p_h, p_u   The outputs are:  90 104 107 62 69 46 13 27 30     Do you have any idea what's going wrong?