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How do I solve $x^{4^x}=4

$How do I solve $x^{4^x}=4$

Your 4x=ln4lnx can be reduced to log4x=4−x or, if you like, logx4=4x, keeping f the same.

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axioms - Directly proving $(-a)^2 = a^2

2 Aug 2016 — I know one can easily prove that (−a)2=a2 from (−a)∗0=(−a)(a+(−a))=(−a)2+(−a)a and one can also show that (−a)a=−a2 (or even (−a)=(−1)∗a), ...

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elementary set theory - Number of points in $[0,1]$ and $[0,2]

Today in class my professor said that the sets [0,1] and [0,2] have the same amount of points. I have some questions about this. Since [0,2]=[0, ...

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$1^3+2^3+...+n^3= $? How I can find formula

15 Oct 2019 — Let f(x) be an integral polynomial of degree d. Let us say, we want to find a formula for S(n)=f(0)+f(1)+⋯+f(n). Knowing ∫xd=xd+1/d+1, one ...

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Proof by induction that $(1^3 + 2^3 + 3^3+\cdots+n^3) = (1 ...

$Proof by induction that $(1^3 + 2^3 + 3^3+\cdots+n^3) = (1 ...$

13 Jun 2014 — By induction hypotesis we have that (1+2+⋯+n)2=(13+23+⋯+n3). We also use another identity, namely (1+2+⋯+n)=n(n+1)/2.

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How do I solve this equation; $x^4+4x-1=0

You may write it as x4+4x−1=(x2+1)2−2(x−1)2=(x2+1)2−(√2(x−1))2. and factorize.

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limits - "Proving" that $0^0 = 1

limits -

The limit of the function yx at [0,0] does not exist. In fact it depends on the path used to approach 0. 0 ...

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Seeking elegant proof why 0 divided by 0 does not equal 1

The reason 0/0 is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals.

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Why does 2^-2 equal 1/2^2?

24 Oct 2014 — The problem in your way of thinking is that when you're thinking about multiplication, you should "start" from 1, whereas you're "starting" from 2.

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functions - Plotting $y=x^{1/y}

$functions - Plotting $y=x^{1/y}$

I stumbled upon/came up with this function: y = x^(1/y), or "the y th root of x equals y" Now I started wondering how this function would look like.

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The solution set of the equation $x^{10}=10^x

$The solution set of the equation $x^{10}=10^x$

1 Dec 2015 — Hard to argue with the graph in the other. But here's one way to look at it: 010=0, 100=1 so 10x>x10 at x = 0. 210=1024>102=100 so 10x

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How can we know the answer to 1-1+1-1+1...? [duplicate]

The series does not converge. But if you treated it as a formal geometric series 1+r+r2+…=11−r and then let r=−1 you would get 12.

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Formal proof for $(-1) \times (-1) = 1

$Formal proof for $(-1) \times (-1) = 1$

Is there a formal proof for (−1)×(−1)=1? It's a fundamental formula not only in arithmetic but also in the whole of math. Is there a proof for it or is it just ...

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How can I factorize $x^{10}+x^5+1

$How can I factorize $x^{10}+x^5+1$

12 Feb 2015 — It turns out that the factor x2+x+1 of x3−1 divides x10+x5+1. Long division then gives x10+x5+1=(x2+x+1)(x8−x7+x5−x4+x3−x+1). The right hand ...

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