# Tagged Questions

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### matrix exponential limit

I'm having litlle trouble here to prove the following statement: "Let $A$ an $n\times n$ matrix (real or complex). Prove that $$\lim_{n \to \infty} \left(I + \frac{A}{n}\right)^{n} = e^{A}.$$ Now ...
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### How to solve an exponential function with multiple addends

Our math teacher gave us the following exponential equation to solve: $3^x+10=2*7^x$ ...and I was stumped. Eventually, the solution given was to graph both sides and find their intersection using a ...
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### Complex exponentiation

So I've got this question that is a bit difficult to ask, since it uses a term in my language that I can't properly translate into English. For $z\in\mathbb{C}^*$ and $a\in\mathbb{C}$ it would be ...
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### Continuous compounding question

A population of rabbits starts out with $100$ rabbits. The growth rate is $11.7$% per day. Determine the exponential equation. Is it $$\mathbb {P(t)} = 100e^{11.7t}$$ Can you guys give me the ...
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### How to solve $5^{n+2} - 5^{n-3} = -2500$ [closed]

How to solve $5^{n+2}- 5^{n-3} = -2500$
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### Logarithm properties doubt

The problem is $\log (5.64)^4$. According to the properties and laws of exponents, $\log (m^r) = r \log (m)$. But since the exponent is outside of the parenthesis in this problem, does it solves by ...
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### Find $x$ in $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot …] x)^{ (((1\cdot x+1)x +1)x +1)x+1…}$

If $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot ...] x)^{ (((1\cdot x+1)x +1)x +1)x+1...}$, and $\large \,\,A = (\sqrt[3]{3\sqrt 3 })^{\frac{\sqrt 3}{3}}$, find $x$ I have ...
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### The domain of fractional exponents

Take the following: $$f(x) = x^{6/4}$$ The domain of this function is all real numbers. This function can be simplified to: $$f(x) = x^{3/2}$$ The domain of this function is all real numbers ...
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### How is this possible? Can someone explain?

My teacher says that $W^{2/7}B^{5/7}=1$ is equivalent to $W^2B^5=1$. Can someone explain this rule to me? Am I always able to just take the variable and raise it to the numerator of the fractional ...
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### Math induction problem (rules of exponents)

Hello I am doing some induction problems, I have to prove that $3^{k+1}-1$ is a multiple of 2. Suddenly they make this statement; $3^{k+1}$ is also $3 * 3^k$. Why is that?
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### zero raised to infinity

I encountered a question where the only condition stated that $t>0$ and was then asked to compare these two quantities $0^t$ $t^0$ The scope of $t$ is $(0,\infty)$ and hence for infinity 1.) ...
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### Why does $(-2^2)^3$ equal $-64$ and not $64$?

The title says it all. Why does $(-2^2)^3$ equal $-64$ and not $64$? This was on my algebra final, and I am completely stuck on how it works.
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### k-fold matrix product

For $k \in \mathbb{N}$, $B,C \in \mathbb{R^{n,n}}$, given the matrices $B,C$ , calculate all powers $B^k$ and $C^k$ I'm a bit puzzled by this task. I assume it's supposed to practice handling ...
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### Exponential equations involving natural numbers at power “x”

Find x : $$4^x+15^x=9^x+10^x(2^x-3^x)(2^x-3^x-5^x)$$
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### Simplifying $y=2^{2/3} + 2^{-1/3}$

I am working on a calculus problem where I have to find the local minimum. The value I got was $$y=2^{2/3} + 2^{-1/3}.$$ I simplified it and got this: $$y=2^{2/3} + \frac{1}{2^{1/3}}$$ ...
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### Algebraic equation problem - finding $x$

$$(x^2 +100)^2 =(x^3 -100)^3$$ How to solve it?
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### Simplifying negative exponents when there are multiple terms.

The problem is to simplify $$\left(\dfrac{1+3z}{3z}\right)$$ I know that when I have $$\dfrac{1}{x}$$ I can bring the $x$ from the denominator to the numerator by changing it to a negative power. How ...
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### How do you compute negative numbers to fractional powers?

My teachers have gone over rules for dealing with fractional exponents. I was just wondering how someone would compute say: $$(-5)^{2/3}$$ I have tried a couple ways to simplify this and I am not sure ...
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### Simplifying $\;x({y^{3}}/{x^{4}})^{1/4}$

I’m a little unsure how to simplify the following expression: $$x\left(\frac{y^{3}}{x^{4}}\right)^{1/4}$$ According to the answer, this should get you $\;\; x y^{3/4} x^{-1} = y^{3/4}$. My ...
How can I prove that $|e^{A}|\leq e^{|A|}$? I guess i'm having trouble with the definition! A is a square (complex or real) matrix.