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
1
vote
1 answer

What contributes more to a increase in value of a exponentiation: a increase of base or exponent?

Firstly, my apologies for being a programmer messing in math land. I was wondering whether the value of a exponentiation is increased more by a increase in the base or exponent (I believe this is a kind of limit?), and how this depends on the…
Shamed programmer
  • 11
1
vote
2 answers

Proving that if $a>1$ and $x>y$ then $a^x>a^y$

I got this assignment for homework and I can't find this anywhere around the web. Prove that if $a>1$ and $x>y$ then $a^x>a^y$. I started the assignment but I'm not sure it's enough: $n>0$ $x=y+n$ $a^x=a\times a\times a\times\dotsb\times a$ ($y+n$…
user109046
  • 11
  • 1
1
vote
1 answer

Formula for the number of digits in the number $2^x$

I'm wondering if there is a formula for the number of digits in $2^x$. For example if $x = 3$ then the number of digits is equal to $1$ because $2^3 = 8$ or for example if $x = 4$ then the number of digits is equal to $2$ because $2^4 = 16$. In an…
java
  • 311
1
vote
1 answer

How to solve this equation with parameters on power?

Please let me know how to solve this equation: $$100^{1-b}=\frac{1}{2}40^{1-b}+\frac{1}{2}200^{1-b}$$ I try to use the trick of $x=e^{\log x}$ But it doesn't work And $b\not=1$
Kenneth Chen
  • 298
1
vote
1 answer

How to solve strange exponential equation?

How would equations of the form $b^x-x^a=0$ be solved for $x$, given $a$ and $b$? For instance, specifically, how would $2^x=x^2$ be solved? Does a method exist?
user87611
1
vote
1 answer

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 exponent?
briteId
  • 353
1
vote
1 answer

Approximate the sum of exponential functions

I'm trying to approximate the sum of $N$ exponential functions as one function. Is it possible to do so, i.e. find function $f$ and constants $a$, $b$, and $c$ such that $$\sum_{k=1}^N c_ke^{a_kx}\approx c f(ax+b)$$
eMathHelp
  • 2,409
1
vote
1 answer

Question about powers

I've been trying to solve this problem, but I can't do it by any means other than brute force, I need help, please. The result is: 6,000.00001 $$\frac{1}{10^{-3}}+\frac{10^2}{2\cdot 10^{-2}}+\frac{10^{-4}}{10}$$
Jose
  • 283
1
vote
0 answers

What is the smallest positive integer that can not be written as a sum of positive integer powers of distinct elements of {1,…,n}?

Lets say you have numbers from 1 to 3, how many numbers can be made using powers of the numbers without the base…
mathiscool
  • 85
1
vote
1 answer

addition of negative exponents in a fraction

i am very confused how to simplify this considering there is addition (and not multiplication) of negative exponents in both numerator and denominator. $$\frac{8^{-4/3} + 2^{-2}}{16^{-3/4}+2^{-1}}$$ Since there is addition, i cannot just do the…
user1078
  • 343
1
vote
0 answers

simplifying exponential equation that has a natural logarithm

I have the following equation: $$y=\exp(C_1-C_2\ln x)$$ where $C_1$ and $C_2$ are constants. I believe that the following is correct: $$y=\exp C_1\exp (-C_2\ln x)$$ $\exp C_1$ is just a constant. I know that the exponent of the natural logarithm of…
rdemyan
  • 97
1
vote
1 answer

Doing repetetive square root of any non negative rational number is 1

When i tried to do the square root repeatedly of any number greater than 0 the calculator gave me 1(I think it was approximate but doing it infinitely many times should give me 1) at a time, so would the square of any number be the original number…
Krave37
  • 455
1
vote
1 answer

Express square root in terms of log 10

I’m trying to help my son with some revision. One of his revision questions uses a formula $$T(n) = 4T(n^\frac{1}{2}) + \log_{10} n$$ To solve the problem he needs to express the $n^\frac{1}{2}$ in the form $\frac{n}{b}$. There’s a hint to define $k…
Kevin O'Donovan
  • 11
1
vote
1 answer

Is there a formula to equally distribute increases over many steps exponentially?

As an example I have: a thing that has 350 steps on step 1 that thing has 800 of x on step 350 that thing has 400,000 of x the increase of x from step 1 to step 2 should be significantly less than the increase from step 349 to 350, but on some…
Serj Sagan
  • 113
1
vote
1 answer

Definition of $x^\alpha$

I've formally defined the power whose base is a positive number and its exponent is a real non-zero number like this: $$x^{\alpha}=\sup\left\{x^p\in\mathbb{R}\mid p\in\mathbb{Q},0
Raúl Filigrana Villalba
  • 61
1 2 3
…
35 36