Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [exponentiation]

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

Exponentiation is a mathematical operation which produces a power $a^n$ from a base $a$ and an exponent $n$. The objects involved are usually numbers, but the procedure can be generalized to matrices, elements in algebraic structures, sets, etc.

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How to solve $x\cdot\mathrm e^x=1$?

Possible Duplicate: Inverse of $y=xe^x$ I would like to solve the equation $x \cdot\mathrm e^x=1$. I know it has an answer, I could find it with a calculator, but I don't remember how to solve it on paper. Any help? edit I know the answer is $x…
SteeveDroz
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What is the right way to calculate a power?

I noticed that there are two solutions for $(-1)^{14/2}$: $((-1)^{14})^{1/2} = 1$ $(-1)^{14/2}=(-1)^7=-1$ What am I doing wrong?
Stav Alfi
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How do we know that $\exp(x)$ agrees with raising a number to a rational power?

This is motivated by an earlier question of mine, in which I realized I was never really presented a definition of $e^x$, or more generally, what it means to raise a (positive) real number to an irrational power. I know that the definition of $a^b$…
Javier
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When is $(a^b)^c $ = $a^{bc}$ true?

I know that in some cases this rule is not true. For example $$((-1)^2)^\frac{1}{2}\ne(-1)^{(2\cdot\frac{1}{2})}$$ So when is this rule true ?
ihebiheb
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How do I reverse engineer this "power of"/exponent?

Take the following: (2)^3 = 8 I understand that this is 2 * 2 * 2 = 8 My question is how do I reverse engineer this if I do not know the power like this: (2)^x = 8 What is the value of x? x could potentially contain a decimal and so could the…
Rupert
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Growth of exponential functions vs. Polynomial

Will $2^x$ take over $x^{1000}$ ? I thought that exponential functions had the fastest growth rate, however, graphing it on wolfram alpha made it seem as if the initial behaviors of the two functions implied $2^x$ never overtook $x^{1000}$.
john
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How do I solve this analytically $3^x=9x$

One of my friends ask me how to solve this equation analytically $3^x=9x$. Looking at it I guess 3 is the answer and I also plot a graph of line $9x$ and the curve $3^x$, they intersect at 3. But, what I want is to give an analytical solution of the…
Hassan Muhammad
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Can $2^k + 2^j$ be expressed as $2^n$?

If we are given $j,k \geq 0, j> k$ and $j,k$ are integers, can $2^j + 2^k$ be ever expressed as $2^n$ where $n \geq 0$ and is an integer? What I said: Suppose it can. Then for some $0 \leq n \in \mathbb{N}: 2^j + 2^k = 2^n$. We know that $j>k$ so…
TheNotMe
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Why does $a^{b}·a^{c}=a^{b+c}$?

Why does $a^{b}·a^{c}=a^{b+c}$ ? I want proof for it, I asked professor and he replied: "I don't know, it's a property anyway that is true and that's all what you need to know."
user120413
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What are the number of integers a $1 \le a \le 100$ such that $a^a$ is a perfect square.

What are the number of integers a such that $1 \le a \le 100$ and $a^a$ is a perfect square. I think the answer should be 51 since a can be 1 and then 2,4,6,...100. Is the answer correct?
user2369284
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Solution to $a\cdot e^{bx} - cx = d$

Similar to the question asked here: Solving $e^x + x = 5$ for $x$ without using a numerical method? How can I get a solution for $a\cdot e^{bx} - cx = d$, where a, b, c, d are constants? Is there a way I can get it in terms of the Lambert W…
Mike Moffatt
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about $3^x+x^3=0$ and other non-trivial equations like this

I was having math class (10th grade) and we were learning about exponential equations, pretty easy, but then i wondered about some mixed equations, like $3^x+x^3=0$. I couldn't solve it, so I looked up the answer in wolfram alpha, and it turned out…
gdor11
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If $a^{1/a}=b^{1/b}=c^{1/c}$ and $a^{bc}+b^{ac}+c^{ab}=729$, find the value of $a^{1/a}$

If $a^{1/a}=b^{1/b}=c^{1/c}$ and $a^{bc}+b^{ac}+c^{ab}=729$, which of the following equals to $a^{1/a}$? $\sqrt[abc]{81}$ $\sqrt{2}$ $\sqrt[abc]{27}$ $\sqrt[abc]{9}$ This question is from the book, Mathematics, Class 9 (The IIT Foundation Series)…
Abhigyan Kumar
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How do I calculate the base of an exponent if I know the result and what it was raised to?

If I know the outcome of a value being raised to a certain power, is it possible to know what the original base was? Example: x ^ 0.25 = 2.5045 What's the proper way to calculate x?
TravisVOX
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Is the sum of two exponential function can be equivalent to a third exponential function?

What will be the sum of two exponential functions $2\exp(4 x) + 3 \exp(5 x)$ equivalent to a third exponential function? Is it possible?
user3563283
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