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.

4326 questions
4
votes
2 answers

Rates of change, compounding rates and exponentiation

I have a very (apologies if stupidly) simple question about rates of change that has been bugging me for some time. I can't work out whether it relates to my misunderstanding what a rate of change is, to my misapplying the method for calculating a…
BillyHarris
  • 81
4
votes
4 answers

How to get exponent of power if base is known?

Sorry for this type of question, but I've forgotten the math basic from middle school, maybe someone can help me out. If I know the result and base, how can I calculate exponent? $2.5 = 10^x$, how would I get the $x$ value of this?
MaaAn13
  • 141
4
votes
3 answers

If $2^{k+1} = 2 \cdot 2^k$ what does $2^{k-1}$ equal?

I know that $2^{k+1} = 2 \cdot 2^k$, but what does $2^{k-1}$ equal? Is it $\frac{2^k}{2}$? Then does $2^{k-2} = \frac{2^k}{2^2}$?
Sam
  • 865
4
votes
4 answers

How to solve equations of this type

My math teacher gave us some questions to practice for the midterm exam tomorrow, and I noticed some of them have the same wired pattern that I don't know if it has a name: Q1. If: $x - \frac{1}{x} = 3$ then what is $x^2 + \frac{1}{x^2}$ equal…
Hatchi Roku
  • 187
  • 7
4
votes
2 answers

Solve the equation $2^x+3^x-4^x+6^x-9^x=1$

I found an interesting equation I don't seem to grasp completely. Solve the equation: $2^x+3^x-4^x+6^x-9^x=1$ Now. I thought the only relevant solution was the integer solutions, but I was sorely mistaken. So if the question was: Find all integer…
einar
  • 377
4
votes
1 answer

Do fractional exponents make sense?

According to my resources, $\sqrt x = x^{\frac{1}{2}}$, and $\sqrt[3] x = x^{\frac{1}{3}}$, etc, or to put it simply, $\sqrt[y] x = x^{\frac{1}{y}}$. However, since I understand an exponent to mean the amount of times a given number (x in this…
J. Allan
  • 143
4
votes
2 answers

Find $x$ in the equation $x^x = n$ for a given $n$

Simply: How do I solve this equation for a given $n \in \mathbb Z$? $x^x = n$ I mean, of course $2^2=4$ and $3^3=27$ and so on. But I don't understand how to calculate the reverse of this, to get from a given $n$ to $x$.
Byte Commander
  • 281
4
votes
3 answers

Solve exponential equation with exponent variables.

Ok, the question is: Solve the following for x: $2^x4^{x-1}=70$ I have just asked Wolfram Alpha, of course though, it supplies an answer without revealing its working. I started to try the product of the bases and the sum of the exponents, giving…
Georgina Davenport
  • 247
4
votes
8 answers

What do you get when you take the square root of a negative imaginary number?

Simply, what do I get when I take the square root of negative imaginary number? But, it cant be an imaginary number since the answer to the $2^{\mathrm{nd}}$ power must equal the original negative imaginary number. So: $$ \sqrt{{-(|x|{_i}})} = y …
Jack G
  • 224
  • 2
  • 17
4
votes
5 answers

Calculating very large powers of $e$

I need to calculate $e^{1763.192674118048}$, but when I try to calculate it directly using Matlab it returns "Inf", i.e. it can't calculate it. How do I calculate this? For what it's worth, just getting the right power of 10 would be accurate…
Jim Clay
  • 403
4
votes
4 answers

How to find the value of $x$ in $x^5=32$

I understand that $2^5=32$ but how would one go about finding it without doing any guessing (what if the numbers were much greater)?
Arthur Alex Karapetov
  • 409
4
votes
1 answer

What are the rules of powers of powers?

What would $2^{3^4}$ equate to? I can think of two rules that may apply: $a^{b^c} = a^{(b^c)}$ (Making $2^{3^4} = 2^{81}\approx2.417\cdot10^{24}$) or $a^{b^c} = (a^b)^c = a^{bc}$ (Making $2^{3^4} = 2^{12} = 4096$) Which of these is true?
otah007
  • 280
4
votes
4 answers

Find $n$ where $n^n$ has $n$ digits

Find n $\in \mathbb{N}$ if $n^n$ has $n$ digits. A problem I ran into today and it seemed interesting. I know $1$, $8$ and $9$ are (the obvious) solutions, but are these the only ones? If they are, how can you prove it? Thanks in advance. EDIT: Yes,…
Robert Badea
  • 396
4
votes
2 answers

powers of 2 in base 3

What is the asymptotic limit of the ratio of $1s$ to $2s$ in the first digits of $2^n$ in base $3$? If the $2^{nd},3^{rd}$ digits etc. were random but equally likely to be $0,1$ or $2$ then the ratio would be $2:1$ since if $2^n$ begins with $2$…
Angela Pretorius
  • 10,200
4
votes
2 answers

How to calculate $(k^x)^{-1} \pmod m$

I'm trying to follow this example of ElGamal's encryption scheme (page 2, slides 3 & 4), but don't understand this step (decryption, step 2): $$(k^x)^{-1} \pmod m$$ Where $$k = 10,\ x = 9,\ m = 13$$ The slide shows that it becomes $$12^{-1}…
Louis Waweru
  • 241
1 2 3
…
35 36