List questions from transcendental-equations

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Number of solution of the equation $2\tan^{-1}|x|\cdot\ln|x|=1$ is

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416

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How to solve equations with both logarithms and square roots, like this: $ax+b\log(x)+c\sqrt{x}+d=0$

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198

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Solving for $\lambda$ in $\frac{k\lambda}{\alpha} \,\tan(\lambda R) -1 = 0$

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Express solutions in terms of $\phi$

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An happy coincidence for the approximate solution of $x \tan(x)=k $?

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44

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Existence of unique root of mixed linear/logarithmic equations

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268

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Prove that $e^{\sin x}-\sin e^x\neq0$ $\forall x\in [-1, \pi]$, an equation in the form $f(g(x))=g(f(x))$

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A solution to a transcendental equation

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67

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Special solution to $a+e^a\ln x = x+e^a\ln a = a+e^x\ln a$

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105

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A good approximation for $\arctan(u \tan (v x))$

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134

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Solve $\frac d{dx}W_{-1}(-1/x)=-1$

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160

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Solution for $ y(x) - ae^{y(x)} = f(x) $ involving Lambert W function

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93

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Closed form solutions to a Gaussian equation

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380

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$e^x+x=0$ has countable infinite many solutions

Published on 29 Apr 2026 - 12:54

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How to solve $a^x + b^x = c \exp(d/e) - f$ for $x$

Number of solution of the equation $2\tan^{-1}|x|\cdot\ln|x|=1$ is

How to solve equations with both logarithms and square roots, like this: $ax+b\log(x)+c\sqrt{x}+d=0$

Solving for $\lambda$ in $\frac{k\lambda}{\alpha} \,\tan(\lambda R) -1 = 0$

Express solutions in terms of $\phi$

An happy coincidence for the approximate solution of $x \tan(x)=k $?

Existence of unique root of mixed linear/logarithmic equations

Prove that $e^{\sin x}-\sin e^x\neq0$ $\forall x\in [-1, \pi]$, an equation in the form $f(g(x))=g(f(x))$

A solution to a transcendental equation

Special solution to $a+e^a\ln x = x+e^a\ln a = a+e^x\ln a$

A good approximation for $\arctan(u \tan (v x))$

Solve $\frac d{dx}W_{-1}(-1/x)=-1$

Solution for $ y(x) - ae^{y(x)} = f(x) $ involving Lambert W function

Closed form solutions to a Gaussian equation

$e^x+x=0$ has countable infinite many solutions

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