# 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.

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### Solution for $(4+2r) x^{(1+r)}−x−1=0$

I am trying to find an analytic solution for the following equation: $$(4+2r) x^{(1+r)}−x−1=0$$ for $$r \in \mathbb{N}$$ and $$\frac{1}{2}<x<1, \space x \in \mathbb{R}$$ I am trying to solve ...
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### Find $x$ such that $\cosh(a + bx) + 1 = cx$

I need to find an analytical solution for $x$ to: $$\cosh(a + bx) + 1 = cx$$ where a,b and c are real parameters. I have tried to tackle this geometrically, by splitting the problem into finding ...
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### Solving Sine Equation [closed]

I'm trying to find all the real solutions of the following trigonometric equation : $$\frac{\sin 3x}{\sin 2x} = A$$ I can see that $x$ is some integer function of $\pi$ , but I cannot find the exact ...
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### Closed form for zeros of a function

I need a closed form for the zeros of $$f(x)=2\sin\left(\frac{\pi}{6}-\frac{\sqrt{3} x}{2} \right)-e^{-\frac{3x}{2}}$$ Putting $x=0$, we see that $f(0)=0$. For the closed form of the remaining zeros ...
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### What is the reason that equations such as $\tan x = 2x$ can only be solved with the help of algorithms?

This is my first StackExchange question: What is the reason that equations such as $\tan x = 2x$, $\cos x = x$, $\sin(x) = x^2$ and other questions that involve the same variable within a ...
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### Approximate inverse of $k=\frac{\log (1-t)}{\log (t)}$

Trying to answer this question where we look for the solution of $$\large\color{red}{t^k+t=1} \qquad \qquad \text{with} \qquad \color{red}{0<k<1}$$ which is more or less the function Lambert ...
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I'm looking for solutions to the equation $$x^2+2^x+x^x = 12$$ Which is satisfied obviously by $x=2$ and somewhat less obviously by $x\approx-3.4512$. By plotting $|z^2 + 2^z + z^z - 12|$ on the ...