For which values of $x$ does $y$ have a value in $x^y=y$? What are the lowest and highest values of $x$? Using geogebra I have found that $x$ should be between $0$ and about $1.4$, but how is an exact answer found? Also, I am only talking about real numbers. Thank you.
2026-04-08 11:37:36.1775648256
For which values of $x$ does $y$ have a value in $x^y=y$?
74 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRA-PRECALCULUS
- How to show that $k < m_1+2$?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Finding the value of cot 142.5°
- Why is the following $\frac{3^n}{3^{n+1}}$ equal to $\frac{1}{3}$?
- Extracting the S from formula
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Solving an equation involving binomial coefficients
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- How to solve algebraic equation
Related Questions in EXPONENTIATION
- exponential equation with different bases; no logarithms
- Is square root of $y^2$ for every $y>0,y\in\mathbb{R}$?
- Definite sum for $(1+a)^n$
- Fractional exponents definition and the additive law of exponents
- Fourth term in the expansion of $(1-2x)^{3/2}$
- Why is $\int_{0}^{t} e^{nt} \mathrm{\ dt} = \frac{1}{n} \left(e^{nt} - 1\right)$? [solved; notation is also faulty in the first place]
- Exponentiation property of the modulo operator
- When are $\left(\frac{a}{b}\right)^c$ and $\frac{a^c}{b^c}$ equivalent?
- How can I rewrite expression to get log out of exponent
- Compare $2^{2016}$ and $10^{605}$ without a calculator
Related Questions in UPPER-LOWER-BOUNDS
- Bound for difference between arithmetic and geometric mean
- Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$
- Bounding Probability with Large Variance
- Connectivity of random graphs - proof $\frac{logn}{n}$ is threshold
- Natural log integral inequality
- Spectrum of a matrix after applying an element-wise function (e.g. elementwise log)
- Majorization form for a given set of integers in some interval.
- Proving $(λ^d + (1-λ^d)e^{(d-1)s})^{\frac{1}{1-d}}\leq\sum\limits_{n=0}^\infty\frac1{n!}λ^{\frac{(d^n-1)d}{d-1}+n}s^ne^{-λs}$
- Upper bound for distribution function of the standard normal distribution
- Show $0 < f'(x) \leqslant \frac{1}{2}$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?