Mathematics Stack Exchange
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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How to solve $0.1=4.8626\cdot xe^{-4.472\cdot x}$

I have stumbled into this equation $0.1=4.8626\cdot xe^{-4.472\cdot x}$ I tried to take the natural logarithm for both side but it didn't help as it will result in $\ln x+x$ which I can't solve. Can someone please show me how to solve this equation…
Jacob
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Is it possible to find solutions to $C=e^{a*x}(A*\cosh(b*x)+B*\sinh(b*x))$

I need to solve a problem in which I find an equation like: $$C=e^{a*x}(A*\cosh(b*x)+B*\sinh(b*x))$$ I would like to express $x$ in function of $C,a,b,A,B$. However I am starting to wonder if it is simply possible to find analytic solution to…
StarBucK
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hint for solving in $t$, the following equation $t^2e^{a^2\,/t} + a^2e^t-12at=0$

Please give me a hint in order to solve in t, the following equation: $$t^2e^{a^2\!/t} + a^2e^t-12at=0$$ where $a=\ln(4)$.
riciu
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Existence of unique root of mixed linear/logarithmic equations

I have functions $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ and $g$ that look like this: \begin{equation} \begin{aligned} f(x) &= Ax + b + g(x) \\ g(x_i) &= -c \log(1/x_i - 1), \quad x_i\in(0,1) \end{aligned} \end{equation} where $A$ is square,…
Tor Anderson
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Transcendental equation $x - c \sin(x)=0$

Hy, well I have a problem with the transcendental equation $x - c \sin(x) = 0$, where $c$ is some positive constant. I tried using Newton's method for finding the roots but it didn't work well. The problem is also the number of solutions, because as…
MarkoBond
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How to solve exponential equation?

I want to mention that it is not my homework, just want to solve for fun. I appreciate any hint how to solve it. The exponential equation is given: $2^x + 3^x = 10000$ My initial thought was to use such transformation: $2^x + 2^{\log_2{3^x}} =…
Alex Aparin
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Closed-form solution for a transcendental-equation with specific coefficients?

I would like to know whether there is a closed-form solution in $x$ for the equation: \begin{align*} &e^{-(\alpha\delta+(\gamma-\phi)\frac{\alpha}{\alpha - 1})x} -\frac{\alpha(r+\delta+\phi-\gamma)}{r+\alpha\delta}e^{-(r+\alpha\delta)x} -…
Marius
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Solving the following equation: $\ln(x)=\frac{x}{1+x}$

I am stuck with solving this equation for $x$: $$\ln(x)=\frac{x}{1+x}$$ Making exponential both sides I get: $$x=\exp\left(\frac{x}{1+x}\right)$$ Then I tried to make a change of variable $x=\frac{1}{z}$ and use omega function. But I reached…
Math1995
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How do I solve $3x^2-e^x=0$?

Solve the following equation for $x$ $$3x^2-e^x=0$$ I tried introducing the logarithm, which gives $$\ln\left(3x^2\right)=x$$ but I can't see how to proceed from here.
maume
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Solving fancy equation

I got stuck on this equation. Could you help me a bit and tell me how should I approach it? The answer of it is 3/4 and -3/4. $$4^{\sin^2(\pi x)}+4^{\cos^2(\pi x)}=-8x^2+12|x|-{1\over2}$$
Nyklu
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Proving the existence of an $x$ such that $(x-a)(x-b)e^{cx} = (x+a)(x+b)e^{-cx}$

I've been working on a PDE problem and I've brought it to the following form: $$ (x-a)(x-b)e^{cx} = (x+a)(x+b)e^{-cx} $$ Where $a, b, c,$ and $x$ are all $> 0$. I'm looking to prove that for any $a, b, c$ fixed we can find an $x$. I have no idea how…
Paul
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To find number of real solutions of equation $\left(\frac {9}{10}\right)^x =-3+x-x^2 $

To find real solutions of $\left(\frac{9}{10}\right)^x = -3 + x -x^2$ I differentiate it to get $\left(\frac {9}{10}\right)^x log(\frac{9}{10})-1 + 2x=0 $ As x goes to $+\infty$ this goes to $+\infty$ and as $x$ goes to $-\infty$ it goes to…
Sophie Clad
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Solving equation for x values

What methods I can use to solve for $x$? And how to do it? $$2x + ( 1 + \cot(x/2) ) / \sin(x/2) + 0.8 = 0$$
Cirvis
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Solving transcendental equation with the unknown on both sides

I need to find the point of intersection between a line segment and a sine wave. Line: $y=-2x+1$ Wave: $y=\sin x$ I put both equations together. $-2x+1=\sin x$ I attempt to isolate $x$. $\sin x+2x=1$ Now I have no idea what to do next.
Daniel
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Showing no algebraic solution exists for a given equation

Let $f(x)=g(x)$ be an equation (1) where at least one of $f$ and $g$ are transcendental functions. Let $h(x)=f(x)-g(x)$. If it can be shown that $h^{-1}(0)$ is non-algebraic, that implies that there is no algebraic solution to (1). How exactly does…
clueless
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