Is it possible when you know some n calculate the x if   $$n = x^x$$  ?  Sorry, I did't even know how this equation is called, any help appreciate.
How to solve following equation: $x^x = C$ as $x, C \in \mathbb{R}_{&gt;0}$. I tried to use exponent and such that: $x\ln x = \ln C$.
Using contracted forms ("don't", "let's") in a formal text How compelled should I feel to use non-contracted forms (do not rather than don't and so on) when writing in a rather formal text, say an academic paper? In one case I am afraid to seem too stilted, in the other, too casual. Are there good guidelines?  And are there differences in this regard between British and American English?  (In this  there was not much more than "Contractions are more frequent in informal than formal contexts".) I installed Android studio some time ago using the following suggested method:     To set up Android Studio on Linux:      Unpack the downloaded Tar file,   android-studio-ide--linux.zip, into an appropriate location   for your applications. To launch Android Studio, navigate to the   android-studio/bin/ directory in a terminal and execute studio.sh. You   may want to add android-studio/bin/ to your PATH environmental   variable so that you can start Android Studio from any directory.   Follow the links to install the SDK outside of the Android Studio   directories.   For whatever reason it has become corrupt and insists I must un-install and re-install. I can't for the life of me find how to un-install it however.  I didn't use apt-get so I can't do apt-get remove.  Does anyone have any suggestions? Simple way to compare processors Today, comparing processors is obviously not just looking at the frequency and the number of cores.  When choosing a new PC, how do you compare processors? Is there some resource, like a site or something that does (not necessarily super-precise) processor comparisons?  Thanks. Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $ Express $\sqrt{3}\sin\theta - \cos\theta$ as: $a\cos (\theta + \alpha) $  Can someone please explain to me how to go about doing this? Did Dolores Umbridge Have Any Association with Voldemort (or Death Eaters) before His Return? How can I revert a config file back to the originally installed version after I have edited it? After MiKTeX update: suddenly all fonts (incl. existing path-referenced ttf files) are not found by fontspec / LuaLaTeX anymore Polynomial in $n$ variables Let $f$ be polynomial in $n$ variables. If we have $f(a_1,\ldots,a_n) = 0, a_i \in S_i$ and $S_1,\ldots,S_n$ are infinite subsets of a field $k$, how can I show that $f=0$? Automatically turn on VPN on computer unlock Ubuntu 18.04 When I wake the laptop from the sleep I need to get the VPN state as I left it (turned on). Can't find the setting of autoconnect in VPN settings... Need some easy way to ask the system to autoconnect the VPN when the internet is available.  Edit based on comments:  Ubuntu 18.04 has no option to Always connect to VPN when using using this connection. MySQL Replication : 1 Slave / Multiple Masters Find The Last 3 digits of the number $2003^{2002^{2001}}$ Find The Last 3 digits of the number $2003^{2002^{2001}}$  BY number theory or otherwise,   Also i would like to ask is there a property observed in the numbers of the form $k^n$, where for some $k, n$ is varied then the digits of $k^n$ are periodic,  for example,  $2^n$,  its last digit is periodic with period 4, its second last digit is periodic $4\cdot 5 = 20$ its third last digit is periodic with periodic with period $20\cdot 5 =100$  I have observed this property with other numbers as well, though period might vary,for different values of $k$. Hoping someone can give me some thoughts on what might be going on here so I can be a bit more informed when I call a plumber.  Situation is, we got our water heater replaced a few years back and ever since this has been an issue. It's more noticeable when it's cold outside it seems, but still seems to be a year round problem. Whenever we  use hot water, we basically run out of it within minutes. In order to get an acceptable amount of hot water (enough to take a 10 minute shower), we literally have to prime the water first. By that I mean I have to turn on the hot water, let it run for a couple of minutes, then turn it off and wait 20 minutes. Then when we go to use the hot water again we'll get hot water for a respectable amount of time. Now I am fairly ignorant to all this, but it seems a 71 gallon hot water heater should be capable of holding enough water to not need to be primed like this. I should be able to take a 30 minute shower, let alone 10 without running out. My shower this morning was decently warm for maybe 2 minutes before it was just warm-ish.   So if anyone can give me some ideas on what might be going on I would appreciate it. We've just put up with this for some years assuming perhaps it was some eco friendly thing. Like the system doesn't maintain much hot water in the tank so it's not always running and only heats water up when you start to use it? I hope that isn't the case though and even so, I should be able to get more hot water out of it. Any help?  UPDATE Sorry everyone, I meant to tell you all that the water heater was gas. The pilot light is lit. I don't recall the specific model though I can look that up if people think it will help. I have actually turned up the thermostat on it above the default and when the water heater is putting out hot water, it can be very hot. Too hot. But again, that requires us to prime it before we get any decent amount of hot water out.  UPDATE 2 Looked it up, I believe this is the model info if that helps anyone: State Select: High Output. Model number: GS675XRRS 300 I was trying to fix my audio problems using suggestions from . One of the comments suggested I execute this and only this:     killall pulseaudio   So I did, and I restarted my computer just in case, but all it did was remove my soundcard and I still couldn't hear anything. Now I don't know how to get my soundcard back.  Please note that I am extremely inexperienced when it comes to Ubuntu. Snap application doesn't see files from another partition I have installed KeePassXC snap package on Ubuntu 17.10. I have multiple linux systems installed on the same drive, so I have made most of my home folders like ~/Documents created as links to a separate ext4 partition (users have same uid so permissions are correct). I tried to open my passwords' database which I have inside Documents, but keepassxc cannot see any files inside Documents. If I put the file in my home folder then it sees it.  Are snap packages able to find files outside from my home folder? Any way to make KeePassXC (and the rest snap packages) access the files at my separate ext4 partition (maybe some configuration somewhere)? How to upgrade to MySQL 8.0? I have a Drupal site 8.6.10 on an Ubuntu server 18.04 with MySQL 5.7.25  I want to update MySQL to version 8.0  Here are the steps I followed :   I backed up my database. I uninstalled MySQL from my server with the commands :  $ sudo systemctl stop mysql $ sudo apt remove mysql-* $ sudo apt purge mysql-* $ sudo apt autoremove $ sudo dpkg -l | grep mysql | grep ii  I added the repository with the command :  $ wget https://repo.mysql.com//mysql-apt-config_0.8.12-1_all.deb  I installed the package with the command :  $ sudo dpkg -i mysql-apt-config_0.8.12-1_all.deb            My problem :   I install MySQL with the command :  $ sudo apt update $ sudo apt install mysql-server    When I do step 5, it installs MySQL 5.7 why does not it install version 8 ? Why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty? How do I resolve "WILL_NOT_PERFORM" MS AD reply when trying to change password in scala w/ the unboundid LDAP SDK? Enumerate non-isomorphic graphs on n vertices In the following the graphs are assumed to be undirected and simple.  1.Enumerate the number of non-isomorphic graphs on $n$ vetrices where $n$ is fixed.  Here are some ideas I had:  The number of labeled graphs is $ 2^{\frac{n(n-1)}{2}} $.  So it is enough to find the number unlabeled graphs on $n$ vertices.I have no idea for this.  2.Enumerate the number of non-isomorphic graphs on $n$ vertices and $m$ edges where $n,m$ are fixed.   Can we find a closed formula for each of this?  Any help?   Thank you! Fontspec causes long underscores My collaborator added \usepackage[no-math]{fontspec} to a document we're working on. The result is that \_ underscores become v. long: cf. pictures below.   \documentclass{article} \usepackage[no-math]{fontspec} \pagestyle{empty}  \begin{document} \textrm{metric\_space} \end{document}   With fontspec:    Without fontspec:   The underscores are about twice as long with fontspec, and also much thinner. My question is, how do I get back to the original width? (Ideally I would like to preserve the thinness -- it looks much nicer than the original.)  In case someone asks, "why are you using \_?", the short answer is that I need to typeset identifiers involving an underscore. See  for an example in context. I'd be happy with using something other than \textrm, if it looks decent in the context of that example. Which of these two phrases has more negative undertone?      "The interview I had was not very good"    or      "The interview I had was not good"