Question

Given $2^x+3^x=4$, find all non-trivial rational $a, b, c$ such that $a^x+b^x=c$, or prove that none exist.

score 56 · Answer 1 · 2026-04-16 17:32:43

56

Views

Given $2^x+3^x=4$, find all non-trivial rational $a, b, c$ such that $a^x+b^x=c$, or prove that none exist.

Published on 16 Apr 2026 - 17:32

score 18 · Answer 2 · 2026-04-16 09:02:13

18

Views

Looking for a symmetric function that has the same asymptote at arbitrary high or low real-valued inputs, and has a real-value at the origin.

Published on 16 Apr 2026 - 9:02

score 54 · Answer 3 · 2026-04-13 03:51:18

54

Views

How to calculate $x,n$ for $x^n=400$

Published on 13 Apr 2026 - 3:51

score 91 · Answer 4 · 2026-04-14 21:08:32

91

Views

How does $a^y = x+\sqrt{x^2+1}$ imply $a^{-y} = -x+ \sqrt{x^2+1}$ and then $x=\sinh(y\ln a)$?

Published on 14 Apr 2026 - 21:08

score 95 · Answer 5 · 2026-04-14 12:09:47

95

Views

BODMAS (exponentiation and brackets)

Published on 14 Apr 2026 - 12:09

score 87 · Answer 6 · 2026-04-16 13:58:06

87

Views

Solving $k e^{k\theta+2k\pi} \cos \theta - e^{k\theta+2k\pi} \sin \theta + \sin \theta = 0$

Published on 16 Apr 2026 - 13:58

score 155 · Answer 7 · 2026-04-14 18:15:06

155

Views

Convergence value of the unique positive real root of ${^{m + 1}x} = {^{m}x} + 1$ as $m$ approaches infinity

Published on 14 Apr 2026 - 18:15

score 153 · Answer 8 · 2026-04-14 17:19:48

153

Views

Something not looking obvious in solving equation $x^y=y^x$ for rational $x$ and $y$.

Published on 14 Apr 2026 - 17:19

score 173 · Answer 9 · 2026-04-11 16:25:52

173

Views

Show that: $e^{\pi}-\pi^{e} >\frac12$ without calculator

Published on 11 Apr 2026 - 16:25

score 152 · Answer 10 · 2026-04-14 06:35:06

152

Views

Inverse of $x^x$ in $(0, \infty)$

Published on 14 Apr 2026 - 6:35

score 54 · Answer 11 · 2026-04-11 13:41:44

54

Views

Checking for a common base of two modular exponentiations with different moduli

Published on 11 Apr 2026 - 13:41

score 82 · Answer 12 · 2026-04-16 12:12:41

82

Views

Find the largest set $A,B$ such that $f:A\rightarrow B, \, \,f(x)=x^x$ has an inverse

Published on 16 Apr 2026 - 12:12

score 140 · Answer 13 · 2026-04-17 15:33:51

140

Views

$x^{x^2} + x^{x^8} =?$ Given $x^{x^4} = 4$

Published on 17 Apr 2026 - 15:33

score 62 · Answer 14 · 2026-04-12 18:48:22

62

Views

Exponential of symmetrical 4x4 matrix

Published on 12 Apr 2026 - 18:48

score 120 · Answer 15 · 2026-04-14 00:53:32

120

Views

How can I solve $e^x=\frac 1{x+5}$?

Published on 14 Apr 2026 - 0:53

List Question

Given $2^x+3^x=4$, find all non-trivial rational $a, b, c$ such that $a^x+b^x=c$, or prove that none exist.

Looking for a symmetric function that has the same asymptote at arbitrary high or low real-valued inputs, and has a real-value at the origin.

How to calculate $x,n$ for $x^n=400$

How does $a^y = x+\sqrt{x^2+1}$ imply $a^{-y} = -x+ \sqrt{x^2+1}$ and then $x=\sinh(y\ln a)$?

BODMAS (exponentiation and brackets)

Solving $k e^{k\theta+2k\pi} \cos \theta - e^{k\theta+2k\pi} \sin \theta + \sin \theta = 0$

Convergence value of the unique positive real root of ${^{m + 1}x} = {^{m}x} + 1$ as $m$ approaches infinity

Something not looking obvious in solving equation $x^y=y^x$ for rational $x$ and $y$.

Show that: $e^{\pi}-\pi^{e} >\frac12$ without calculator

Inverse of $x^x$ in $(0, \infty)$

Checking for a common base of two modular exponentiations with different moduli

Find the largest set $A,B$ such that $f:A\rightarrow B, \, \,f(x)=x^x$ has an inverse

$x^{x^2} + x^{x^8} =?$ Given $x^{x^4} = 4$

Exponential of symmetrical 4x4 matrix

How can I solve $e^x=\frac 1{x+5}$?

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