Question

An (im)possible closed form solution to $x^{x^{-3}}=2^{x^{-3}-2^{x-3}}$

score 298 · Answer 1 · 2026-04-04 07:35:37

298

Views

An (im)possible closed form solution to $x^{x^{-3}}=2^{x^{-3}-2^{x-3}}$

Published on 04 Apr 2026 - 7:35

score 129 · Answer 2 · 2023-10-09 09:13:42

129

Views

Find all integer quadruples $(a,b,x,y)$ satisfying $a^x-b^y=(ab)^{x-y}$

Published on 09 Oct 2023 - 9:13

score 128 · Answer 3 · 2026-03-27 13:01:59

128

Views

Does a transcendental number raised to the power of an irrational algebraic number, always result in an algebraic number?

Published on 27 Mar 2026 - 13:01

score 100 · Answer 4 · 2023-10-11 07:57:53

100

Views

Is it possible to prove that $(x+1)\cdot\ln(x-1) > x\cdot\ln(x)$ for all integer values of $x>4$?

Published on 11 Oct 2023 - 7:57

score 146 · Answer 5 · 2026-04-01 14:22:43

146

Views

Solve for $x$: $\frac{16^x-25^x}{8^x-5^x}$

Published on 01 Apr 2026 - 14:22

score 78 · Answer 6 · 2023-10-14 21:26:29

78

Views

Why does changing $dx$ to $dt$ change the value of $\frac{d}{dx}e^{x^2}$?

Published on 14 Oct 2023 - 21:26

score 53 · Answer 7 · 2026-03-25 22:25:08

53

Views

Convergence of Lie Series

Published on 25 Mar 2026 - 22:25

score 117 · Answer 8 · 2023-10-21 14:58:49

117

Views

How to evaluate: $\displaystyle\int_0^1\frac{xe^x-e^x}{x^2-2xe^x+e^{2x}}dx$

Published on 21 Oct 2023 - 14:58

score 72 · Answer 9 · 2023-10-23 14:07:23

72

Views

How to solve this non-algebraic equation: $e^x-5x+7=0$

Published on 23 Oct 2023 - 14:07

score 64 · Answer 10 · 2023-10-23 17:04:59

64

Views

I need help with this following exponential equation

Published on 23 Oct 2023 - 17:04

score 100 · Answer 11 · 2023-10-24 13:21:25

100

Views

A very fun integration problem: Solving for $a$ in $\displaystyle\int_0^2(xe^a+ax)dx=0$

Published on 24 Oct 2023 - 13:21

score 107 · Answer 12 · 2026-03-31 08:38:32

107

Views

Infinitely decreasing exponents

Published on 31 Mar 2026 - 8:38

score 129 · Answer 13 · 2026-04-02 06:44:57

129

Views

Power-series expansion of $\mathrm{e}^{\frac{z}{2}(t-\frac{1}{t})}$

Published on 02 Apr 2026 - 6:44

score 121 · Answer 14 · 2026-03-27 06:17:10

121

Views

Numbers such that $ \sqrt{ {a_{1}}^{a_{2}^{...^{a_{n}}}}} = a_{1} a_{2} \dots a_{n}$

Published on 27 Mar 2026 - 6:17

score 111 · Answer 15 · 2023-10-27 17:12:29

111

Views

Does the value of $(-37)^{1/33}$ exist?

Published on 27 Oct 2023 - 17:12

List Question

An (im)possible closed form solution to $x^{x^{-3}}=2^{x^{-3}-2^{x-3}}$

Find all integer quadruples $(a,b,x,y)$ satisfying $a^x-b^y=(ab)^{x-y}$

Does a transcendental number raised to the power of an irrational algebraic number, always result in an algebraic number?

Is it possible to prove that $(x+1)\cdot\ln(x-1) > x\cdot\ln(x)$ for all integer values of $x>4$?

Solve for $x$: $\frac{16^x-25^x}{8^x-5^x}$

Why does changing $dx$ to $dt$ change the value of $\frac{d}{dx}e^{x^2}$?

Convergence of Lie Series

How to evaluate: $\displaystyle\int_0^1\frac{xe^x-e^x}{x^2-2xe^x+e^{2x}}dx$

How to solve this non-algebraic equation: $e^x-5x+7=0$

I need help with this following exponential equation

A very fun integration problem: Solving for $a$ in $\displaystyle\int_0^2(xe^a+ax)dx=0$

Infinitely decreasing exponents

Power-series expansion of $\mathrm{e}^{\frac{z}{2}(t-\frac{1}{t})}$

Numbers such that $ \sqrt{ {a_{1}}^{a_{2}^{...^{a_{n}}}}} = a_{1} a_{2} \dots a_{n}$

Does the value of $(-37)^{1/33}$ exist?

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