List questions from exponential-function

Published on 07 Oct 2018 - 16:22

266

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

Published on 25 Mar 2026 - 4:43

94

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Find $\lim_{x \to 0^{+}} \frac{\pi^{x\ln x} - 1}{x}$ if it exists .

Published on 26 Mar 2026 - 14:34

97

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$a + b = 2$ implies $a^c + b^c \ge 2$ for any real $c \ge 1$

Published on 27 Mar 2026 - 0:03

337

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Find range of exponent

Published on 25 Mar 2026 - 17:37

1.2k

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Prove $F_{n+1} ≤ (\frac74)^n $, where $F_n$ are Fibonacci numbers

Published on 25 Mar 2026 - 22:05

111

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Not clear in one step in the inequality for the proof LCM$(1,2,\dots,n) < 3^n$

Published on 22 Mar 2026 - 14:23

98

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Prove that $e^{\frac12i\,\text{gd}(\pi t)}\cos^\frac12(\text{gd}(\pi t))=\frac{1+i}{e^{\pi z}+i}e^{\frac{\pi z}2}$

Published on 26 Mar 2026 - 8:02

85

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What are some statistical distributions with the irrational numbers e and pi in their functions? (apart from the most common - Normal, Poisson)

Published on 25 Mar 2026 - 16:03

32

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Even out a numerical curve

Published on 26 Mar 2026 - 7:57

85

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What is the mathematical approach of inversing a function resulting in a piece-wise solution?

Published on 25 Mar 2026 - 1:27

226

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Solve $9^x-2^{x+\frac{1}{2}}=2^{x+\frac{7}{2}}-3^{2x-1}$

Published on 14 Oct 2018 - 15:36

356

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Exponents and Log

Published on 15 Oct 2018 - 2:48

517

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Express in exponential form : 5 bacteria triple every 15 minutes. How many after 3 hours?

Published on 15 Oct 2018 - 3:00

226

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Proving inequalities hold when applying exponentials

Published on 15 Oct 2018 - 5:29

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Solving $2^x + 3^x = 12$

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

Find $\lim_{x \to 0^{+}} \frac{\pi^{x\ln x} - 1}{x}$ if it exists .

$a + b = 2$ implies $a^c + b^c \ge 2$ for any real $c \ge 1$

Find range of exponent

Prove $F_{n+1} ≤ (\frac74)^n $, where $F_n$ are Fibonacci numbers

Not clear in one step in the inequality for the proof LCM$(1,2,\dots,n) < 3^n$

Prove that $e^{\frac12i\,\text{gd}(\pi t)}\cos^\frac12(\text{gd}(\pi t))=\frac{1+i}{e^{\pi z}+i}e^{\frac{\pi z}2}$

What are some statistical distributions with the irrational numbers e and pi in their functions? (apart from the most common - Normal, Poisson)

Even out a numerical curve

What is the mathematical approach of inversing a function resulting in a piece-wise solution?

Solve $9^x-2^{x+\frac{1}{2}}=2^{x+\frac{7}{2}}-3^{2x-1}$

Exponents and Log

Express in exponential form : 5 bacteria triple every 15 minutes. How many after 3 hours?

Proving inequalities hold when applying exponentials

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