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Mathematics Stack Exchange

Questions tagged [transcendental-equations]

Transcendental equations are equations containing transcendental functions, i.e. functions which are not algebraic. An algebraic function is a function that satisfies a polynomial equation whose terms are themselves polynomials with rational coefficients.

Transcendental equations are equations containing transcendental functions, i.e. functions which are not algebraic. An algebraic function is a function that satisfies a polynomial equation whose terms are themselves polynomials with rational coefficients.

448 questions
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Solution of complicated transcendental equation

I am trying to reproduce a result from https://arxiv.org/pdf/0811.2230.pdf Particularly, I am trying to compute the total inelasticity and make the same plot as in fig.1. However, I am unable to explicitly express $K_\theta$ from eq.21, and…
Tomáš
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Issue solving an equation

I'm at lost trying to solve the following equation : $$B\cdot x^{\frac{2}{3}}+C\cdot x^{\frac{1}{2}}=D$$ My research lead me to think that it's a transcendental equation but I don't know how to solve it... Thanks for reading, Regards, 76MPaul
76MPaul
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Uniqueness of solution for transcedental equation on the open set

What is the best way to prove that x=a is the unique solution for the equation $$\frac{2a}{x} = \exp (2-\frac{2x}{a}) +1$$ for $x>0$ ? Intermediate Value Theorem does not work since the interval is open. Thank you for your time.
user314849
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Show that a given transcendental function is uniquely solvable.

I'm looking for a theorem to use to show that the following transcendental function is uniquely solvable. I don't care really about the solution. $$ \rho = \mathrm{e}^{x-\rho t} $$ How might I show this function is uniquely solvable for $\rho$?
Anthony P
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Solving simple transcendental equations

Is there a way (excluding solving by graphing the two functions) to solve an equation like $\sin x = \ln x$ ?
Ramūnas Genys
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Help solving a functional equation that involves exponentiation, ratios, and absolute values

I've encountered the following beast in my research: $$\frac{f(|x|)}{f(|x-\delta|)}=\operatorname{Exp}\left(a+bx^2-\frac{f(|x+\delta|)}{f(|x|)}\right)$$ Here, $x$ and $\delta\neq0$ are real numbers, and $a$ and $b$ are real constants. I am wondering…
M.B.M.
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Ugly expression. Cant tell if I can simplify. Is there a general method for simplifying basic algebraic expressions?

Let $\rho, \omega, c > 0$ and let $\alpha \in [0,1]$. I have managed to calculate \begin{align*} \frac{\rho}{\alpha x^{\alpha-1}y^{1-\alpha}}&= \eta\\ \frac{\omega}{(1-\alpha) x^{\alpha}y^{-\alpha}}&= \eta\\ \left(\frac{\rho}{\omega}…
Stan Shunpike
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Proof that for $\alpha > 0$ and $\tau \geq 0$ , P($s$) = $(s+\alpha+ e^{-s\tau})$ has no solution less than zero

P($s$) = $(s+\alpha+ e^{-s\tau})$ Proof that for $\alpha > 0$ and $\tau \geq 0$ the polynomial has no solution less than zero. I am having difficulty proving that for $\alpha > 0$ and $\tau \geq 0$, the polynomial below doesn't lead to a real…
MEssam
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Solving a transcendental equation

How do I go about solving the following equation? $$x = A + B \log\left( \cosh\left(\frac{x}{C}\right)\right)$$
jdizzle
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How to solve $\log n = \frac{\log 2}{10} \sqrt{n}$

I need to solve $\log n = \frac{\log 2}{10} \sqrt{n}$. I know it is a transcendental function and also hear about generalizes Lambert function (Lambert W-function) could help me to solve it. But I have no idea about how to apply it.
Daniel Ferreira Castro
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Explicit solution of the following equation possible?

Is it possible to obtain an explicit solution for $K$ for the following equation? $$(e^K - 1)(e^{\beta K} - 1) = q$$ for $0\leq q \leq 4$ and $0\leq \beta \leq 1$ For $\beta=1$ one gets $K=\log{\left(1+\sqrt{q}\right)}$. EDIT Actually this…
antarcticfox
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Solve differential equation solution?

I want to solve for $Y(x)$: $$ Y(x) = A - Bx + C\ln(A/Y(x)) $$ where $A$, $B$, and $C$ are defined. Not sure how to go about this. I'm tempted to treat $x$ and $Y(x)$ independently and solve them as roots, but I don't think that would be okay.
user3085446
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Analytical expression for the height of a circular segment

The area of a circular segment is $A=\frac{R^2}{2}\left(\theta - \sin\theta\right)$ Considering $A$ and $R$ known, can you find an analytical expression for $\theta$? Or am I forced to solve it numerically (e.g. Fixed-point iteration)?
remus
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Solving the equation $-e^{-i2k\ell}=\frac{k-1}{k+1}$ for $k$

I am trying to solve the following equation for $k$: \begin{equation*} -e^{-i2k\ell}=\frac{k-1}{k+1}\, , \end{equation*} where $\ell$ is a positive number (constant). I would like to know how the solutions of $k$ look like. I expect it to be an…
putti.123
  • 339
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Nolinear system of equations.

$$ \left\{\begin{array}{l} x^y = y^x \\ x-y\cdot\log_xy=(x+y)\cdot\log_xy \end{array} \right. $$ Thanks for your time!
Florin M.
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