How do I solve equations of the form $kx=e^x$ for $x$?  E.g. how would I solve $3x=e^x$?    I have tried using logs  $$ \begin{align*} 3x&amp;=e^x \\ \ln3x&amp;=x\\ \ln3+\ln{x}&amp;=x\\ x-\ln{x}&amp;=\ln3 \end{align*} $$  but it doesn't look like this is going to get me anywhere.
If I want to solve the equation $4x = e^x$, is there a way to solve for $x$ without graphing and looking for intersection?
I'm a Sri Lankan passport holder. I'm planning to travel to China in January and have to transit in Malaysia. I wonder whether I can obtain a Malaysian transit visa in KLIA 2 when I'm flying back to Sri Lanka. Why can I only change my Stack Overflow name once every 30 days? I have a  on Stack Overflow. I recently decided to change the name on my profile. I did this, but I made a spelling mistake! I wrote "Kryton" instead of "Kryten"! When I tried to fix this, a message came back saying that I can only change my profile name every 30 days. Why? Is there any way I can fix my profile name? Quadratic models with R. The use of poly(..) and I(..) functions (R-language) What causes the different results below?    var1 = c(0.04875,0.13725,0.28350,0.50975,0.77425,0.94700,0.05325,0.14050,0.29725,0.51525,0.79000,0.95400,0.04625,0.15250,0.29000,0.53300,0.79825,0.95225,0.05025,0.14625,0.28800,0.52625,0.78200,0.95925,0.04700,0.14225,0.30325,0.53500,0.79325,0.95875,0.04775,0.13850,0.28675,0.54250,0.78300,0.95175,0.05150,0.12725,0.30175,0.54725,0.79475,0.96275,0.05375,0.14100,0.30050,0.53275,0.78100,0.96175,0.05450,0.15300,0.29650,0.52850,0.80100,0.95675,0.05425,0.13975,0.30875,0.56025,0.80575,0.96100,0.05100,0.15350,0.31175,0.53300,0.78900,0.96000,0.04650,0.13525,0.29600,0.53625,0.78475,0.96375,0.05375,0.13900,0.29600,0.53725,0.78700,0.95800,0.05075,0.14350,0.29225,0.54525,0.80275,0.95800,0.05050,0.13200,0.29850,0.52700,0.80525,0.96150,0.05150,0.14050,0.29450,0.54375,0.79450,0.96375,0.05375,0.13525,0.30475,0.55250,0.79425,0.96025,0.04950,0.14500,0.29425,0.52250,0.78475,0.95650,0.05225,0.14425,0.29225,0.53150,0.80425,0.95375)  var2 = c(1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6)  var3 = c(4,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,10,10,10,10,10,10,12,12,12,12,12,12,14,14,14,14,14,14,16,16,16,16,16,16,18,18,18,18,18,18,20,20,20,20,20,20,22,22,22,22,22,22,24,24,24,24,24,24,26,26,26,26,26,26,28,28,28,28,28,28,30,30,30,30,30,30,32,32,32,32,32,32,34,34,34,34,34,34,36,36,36,36,36,36,38,38,38,38,38,38,40,40,40,40,40,40)   summary(aov(var1~as.factor(var2)*var3)) summary(aov(var1~as.factor(poly(var2,1))*poly(var3,1)))   I might not understand well how poly(..) and I(..) work. Could you give me some hints about these two functions?  (I aim to create models of different degree (quadratic, cubic, etc..) and compare their BIC (or AIC)). Loading a package conditionally How does a one-sided glass work? How does a  work? If seen from the outer side, we can see through thinking it is transparent, while if seen from the inside, the glass acts as a mirror. How? Why can other users see the files in my home folder? Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$ I came across this question:   From the comments, Joren said:     L'Hopital Rule is easiest: $\displaystyle\lim_{x\to 0}\sin x = 0$ and $\displaystyle\lim_{x\to 0} = 0$, so $\displaystyle\lim_{x\to 0}\frac{\sin x}{x} = \lim_{x\to 0}\frac{\cos x}{1} = 1$.   Which Ilya readly answered:     I'm extremely curious how will you prove then that $[\sin x]' = \cos x$   My question:  is there a way of proving that $[\sin x]' = \cos x$ without using the limit $\displaystyle\lim_{x\to 0}\frac{\sin x}{x} = 1$. Also, without using anything else $E$ such that, the proof of $E$ uses the limit or $[\sin x]' = \cos x$.    All I want is to be able to use L'Hopital in $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}$. And for this, $[\sin x]'$ has to be evaluated first.    Alright... the definition that some requested.   Def of sine and cosine: Have a unit circumference in the center of cartesian coordinates. Take a dot that belongs to the circumference. Your dot is $(x, y)$. It relates to the angle this way: $(\cos\theta, \sin\theta)$, such that if $\theta = 0$ then your dot is $(1, 0)$.  Basically, its a geometrical one. Feel free to use trigonometric identities as you want. They are all provable from geometry. How to find users by name Process substitution and pipe In  it says     To make gradient descent work correctly, we need to choose the learning rate η to be small enough that Equation (9) is a good approximation. If we don't, we might end up with $\Delta C&gt;0$, which obviously would not be good! At the same time, we don't want $\eta$ to be too small, since that will make the changes $\Delta v$ tiny, and thus the gradient descent algorithm will work very slowly. In practical implementations, $\eta$ is often varied so that Equation (9) remains a good approximation, but the algorithm isn't too slow. We'll see later how this works.   But just a few paragraphs before we established that $\Delta C\approx−\eta\nabla C⋅\nabla C=−\eta\|\nabla C\|^2$ is obviously always negative (for positive $\eta$). So how can $\Delta C$ be positive if we don't choose a small enough learning rate? What is meant there? HTML form readonly SELECT tag/input According to HTML specs, the select tag in HTML doesn't have a readonly attribute, only a disabled attribute. So if you want to keep the user from changing the dropdown, you have to use disabled.  The only problem is that disabled HTML form inputs don't get included in the POST / GET data.  What's the best way to emulate the readonly attribute for a select tag, and still get the POST data? How many connected components does $\mathrm{GL}_n(\mathbb R)$ have? I've noticed that $\mathrm{GL}_n(\mathbb R)$ is not a connected space, because if it were $\det(\mathrm{GL}_n(\mathbb R))$ (where $\det$ is the function ascribing to each $n\times n$ matrix its determinant) would be a connected space too, since $\det$ is a continuous function. But $\det(\mathrm{GL}_n(\mathbb R))=\mathbb R\setminus\{0\},$ so not connected.  I started thinking if I could prove that $\det^{-1}((-\infty,0))$ and $\det^{-1}((0,\infty))$ are connected. But I don't know how to prove that. I'm reading my notes from the topology course I took last year and I see nothing about proving connectedness... number of vertices in a self-complemntary graph Problem: Prove that the number of vertices of a self-complementary graph must be congruent to 0 or 1 modulo 4. I think my starting point would be that P4 and C5 are self-complementary and proceed by induction by adding P4s. I established the first step in a previous problem, but I need help on the induction step. i.e. proving that adjoining P4 will indeed yield a self-complementary graph. "Can’t help but" vs. "can help but" Is "can’t help but" considered to be a confused mix of the expressions "can but" and "can’t help"? If not, what is the difference between "can help but" and "can’t help but"? Enable automatic deletion of old, unanswered, zero-score questions after a year? Related to Meta Super User efforts:  and Meta Server Fault efforts:  We already auto-remove negatively voted unanswered old questions automatically after 30 days, network wide, with no human intervention required. I was thinking we might extend that to remove old, unanswered zero score questions... based on the following criteria:  fewer than (question age in days * 1.5) views 0 score or lower, or 1 score or lower if the original author is deleted no answers 1 comment or fewer asked more than 1 year ago (thus based on creation date, not last activity date, so , or a user editing it, does not give a doomed question 365 more days of zombie &quot;life&quot;)  See the results of this query on:  (10509) |  (787) |  (650) This query has been refined based on the comments, and this is the final version that will roll out tonight. Every site in the network (except metas) will automatically delete old questions that meet this criteria from this point forward. How to cleanup deadlinks I was reading some answers about ruby and there are a lot of links to _why's sites.  and took all his sites with him.  Almost every introduction question about ruby will include at least one or two links to one of his sites. Examples:          With a bit more effort I could probably find more questions with a lot of deadlinks.  My suggestion for discussion was, what would be a good way to solve deadlinks in the answers/comments? Not every site _why created has resurfaced somewhere else, but some could be replaced by new links.  But I wanted the discussion to go beyond this specific problem of deadlinks in the ruby answers, an automatic solution would be to let the links be scanned in a batch and when found dead be replaced by a google cache or webarchive version of the page, and perhaps mark it so that the community can replace the link with an alternative? Can non basic lands be tapped for colorless mana? For example,  has a mana fixing ability, but it doesn't say you can tap it for mana. Other non-basic lands have a mana ability listed on the card. Should I assume that Evolving Winds cannot be tapped for mana?  Basic lands don't have mana tapping abilities listed, but are assumed you can tap them for mana of the color they represent. How do I mount .vhd file? I'm using 13.04 Raring amd64 and I need to mount a .vhd file on my ubuntu. I've googled about it and found that virtualbox-fuse package is the answer.  But the package was deleted from apt repository. Is there any way to install the package w/ 13.04? or is there any alternative to virtualbox-fuse? Countable sets have the same cardinality as the natural numbers (or a subset of the natural numbers, depending on who you ask).  Can one make the same claim about uncountable sets and real numbers?  In other words, do all uncountable sets have same cardinality as real numbers? "more than one does" or "more than one do"? However, if no x satisfies the equation or more than one x does—that   is the solution is not unique—the problem is said not to be well   posed.   In the line(source: ) above it uses "more than one does", but logically and intuitively it should be "more than one do" since "more than one" means two or more, then it is plural. I have tried my best to interpret it as it is, but hardly can I convince myself to make "more than" collocate with "does" as an adv., which may only make it make sense.