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.

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How many solutions does this equation have for different values of l?

I am trying to solve the following equation for $k$: \begin{equation} e^{2i\cdot l\cdot k}=\frac{k-1}{k+1} \, , \qquad l\in \mathbb{R} \end{equation} I already know that the equation restricts the possible $k$ values to a discrete set and forces…
putti.123
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How to solve $5^x-4^x-3^x-2^x-26=0$ by hand?

Is there a way to solve $5^x-4^x-3^x-2^x-26=0$ by hand? Added for clarity: I can test values and quickly find $x=3$ is a solution and can show that it is the only one. What I am curious about is if there is some nice more general method to arrive at…
David Taub
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Are there any examples of closed form solutions of transcendental equations

An ambitious and amateur question regarding closed form solution of equations involving finite exponential terms.
user121471
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Is there anything known about this transcendental equation?

I came across the following problem: solve $(a^2+s^2)\sinh s + 2 b s = 2 s \cosh s$ for $s$, with $a$ and $b$ real parameters. Is there anything known about the solution(s) of this problem?
arovai
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Solving $(x+y) \exp(x+y) = x \exp(x)$ for $y$.

While thinking about the Lambert $W$ function I had to consider Solving $(x+y) \exp(x+y) = x \exp(x)$ for $y$. This is what I arrived at: (for $x$ and $y$ not zero) $(x+y) \exp(x+y) = x \exp(x)$ $x\exp(x+y) + y \exp(x+y) = x \exp(x)$ $\exp(y) + y/x…
mick
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Why a transcendental equation can not be analytically evaluated

I'm reading this book in Classical Mechanics and they derive an equation for the time a projectile takes to reach the ground once is fired (accounting for air resistance): $$T=\frac{kV+g}{gk}(1-e^{-kT})$$ I do not have any questions on how they…
Hermes Chirino
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Always transcendental? $a + b e^{-x} - f(x) = 0$

I want to choose $f(x)$ such that the equation $$a + b e^{-x} - f(x) = 0$$ is analytically solvable. Ideally, I want $f(x)$ to be some function that is symmetric about 0 and everywhere positive, like $x^2$ or $|x|$. Is there a function with these…
jdizzle
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Finding roots to transients

I understand how to solve 2 element transient but am having some problems with 3+ element transients. Specifically I'm trying to solve this equation: $$737280 e^{-2400t}-576000 e^{-1500t} + 46080 e^{-600t}=0$$ Whenever I use WolframAlpha it always…
ToBeen
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Solution for Transcendental Equation $B+x\sin{\left(\frac{A}{x}\right)}=0$

I am trying to solve a transcendental equation of the form: $$B+x\sin{\left(\frac{A}{x}\right)}=0,$$ where both $A$ and $B$ are constants. What would be the best approach to solve it?
alok1974
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Is there a closed form for the values $x$ where $f(x) = 0$ and when $f(x) = 1$

I posted an answer to the question An Integral Involving The Inverse Of $f(x)$ and my answer depends on knowing where the function $f(x)$ is $0$ or $1$. The function itself is $$f(x) = \log x - \log \cos x + x \tan x$$ on $x \in (0,\pi/2)$. On this…
Alexander Vlasev
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Find the smallest number b such that the function

Find the smallest number b such that the function $f(x)=x^3+7x^2+bx+4$ is invertible. Evaluate $\frac{\mathrm{d}}{\mathrm{d}x}(f^{-1})(4)$ using that $b$.
Illuminati
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Number of real solution of $2^{\sin(x)}-2e^{-\sin(x)}=2$ is

Number of real solution of $\displaystyle 2^{\sin(x)}-2e^{-\sin(x)}=2$ is What I try :: Put $\displaystyle 2^{\sin(x)}=t$, Then $\displaystyle t-\frac{2}{t}=2\Longrightarrow t^2-2t-2=0$ $\displaystyle t^2-2t+1=3\Longrightarrow…
jacky
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How to solve one unknown equations like $15^x = x^{16}$ or $x^x = 1991$ etc...?

I am curious how to solve equations like $15^x = x^{16}$ or $x^x = 1991$. Yes, of course Wolfram Alpha or Matlab can calculate it, or it can be approximated (as we learned in school). But are there any other solution methods? They can be transformed…
lajos.cseppento
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How can you determine if a transcendental equation has elementary solutions or not?

I want(ed) to analytically solve the transcendental equation $e^{\sin(x)} = \sin(e^x)$ for a closed form solution. My working so far…
user1112591
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What is a transcedental Equation?

I was studying equations, and came across the term Transcedental being use for equations of the form, $$ \sin(x) -e^{x} + x^{2 }= 0 $$ From what I understand, the equations involving terms like exp, sin are called transcedental. I also googled and…
Achal_Jain
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