Questions tagged [exponentiation]

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

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How can $x^0=1$ be proved with a real life experiment?

I saw that $x^0=1$ proof is $\displaystyle x^{a-a} = \frac{x^a}{x^a} = 1.$ However I don't find this a convincing proof. How can someone prove this without using the fraction above? or, Is that ...
48 views

I need to make an exponental equation with subtracting

I have this equation $$X(1+0.2)^Y$$ Which is simply adding 20% every $Y$ month for the $X$. For example $$100(1+0.2)^1 = 120$$ $$100(1+0.2)^2 = 144$$ What I want to do is cutting or rebating 10 ...
34 views

Find the exponent of a number with base 2

I am trying to write a program for which I need to map the following data: in out 1 -> 0 2 -> 1 4 -> 2 8 -> 3 16 -> 4 etc. I've figured out ...
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Do cyclic groups appear as symmetry groups of exponentiation-only terms?

Let $\mathfrak{E}=(\mathbb{N};\mathsf{exp})$ be the structure consisting of the natural numbers together with exponentiation. Given a term $t$ in the language of $\mathfrak{E}$ - that is, an ...
91 views

An algebra question from usa math contest [closed]

Question- if k is even number then for what value of x and y , $$x^{2k} - (xy)^k + y^{2k} =0$$ I dont have any knowledge about this math, i generally solve normal math . Please anyone give me a hint ...
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Powers of Fourier series

I have a problem with the Fourier series of a Jacobi elliptic function. Let us assume $$\operatorname{sn}(x,i)=\sum_{n=0}^\infty a_n\sin\left((2n+1)\frac{\pi}{2K(i)}x\right)$$ with $a_n$ known (...
116 views

Is $\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^n+1}$a complex number? What is happening?

While computing the integral $$\displaystyle\int_0^1{\displaystyle\sum_{n=1}^{\infty}x^{(2^n)}dx}$$ I easily got to $$\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^n+1}$$ Since this was getting ...
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Solving equation where unknown is on the exponent

In general is there a systematic of solving equations of the following form: $$a \exp(bx^2+cx)+ d \exp(x) = e$$ where $a$, $b$, $c$, $d$, $e$ are constants and $x$ is the unknown.
Is it correct that $b^a<a^b$, where $b>a>e$? And how do I prove it? [closed]
After watching many videos about "which number is bigger?", I decided to make the following inequality: $$b^a<a^b$$ where $b>a>e$. Is this inequality correct? If it's not correct, ...