Question

Is there any way express $2^{6/x} - 2^{x+1} + 12 = 0$ taking $2^x$ as some variable, say $a$?

score 75 · Answer 1 · 2023-08-08 12:47:03

75

Views

Is there any way express $2^{6/x} - 2^{x+1} + 12 = 0$ taking $2^x$ as some variable, say $a$?

Published on 08 Aug 2023 - 12:47

score 99 · Answer 2 · 2023-08-08 16:21:37

99

Views

Find x and y for $11^x=5*2^y+1$

Published on 08 Aug 2023 - 16:21

score 88 · Answer 3 · 2023-08-10 16:28:05

88

Views

Solve the equation in integers numbers $3x^2-2xy-7=y^2$.

Published on 10 Aug 2023 - 16:28

score 152 · Answer 4 · 2023-08-11 10:36:34

152

Views

help me with idea to understand: Determine the real number x for which the value of the expression $E(x)=\sqrt{x^2-4x+5}+\sqrt{x^2-6x+13}$ is minimum

Published on 11 Aug 2023 - 10:36

score 66 · Answer 5 · 2026-02-23 08:27:02

66

Views

If $a,b,c$ are nonzero natural numbers that verify the relation $a^2+b^2=c^2$, show that $a^n+b^n<c^n$.

Published on 23 Feb 2026 - 8:27

score 52 · Answer 6 · 2023-08-15 16:57:09

52

Views

Is this a unique property of power functions?

Published on 15 Aug 2023 - 16:57

score 55 · Answer 7 · 2023-08-16 03:24:04

55

Views

Is there a way to simplify this exponent?

Published on 16 Aug 2023 - 3:24

score 82 · Answer 8 · 2023-08-17 21:30:55

82

Views

If $a,b,x\in\mathbb{R}^+$ and $a<b$ then $a^x<b^x$

Published on 17 Aug 2023 - 21:30

score 44 · Answer 9 · 2026-03-31 10:07:32

44

Views

Simplification - Power of diagonal matrix and circulant matrix

Published on 31 Mar 2026 - 10:07

score 75 · Answer 10 · 2023-08-21 05:09:18

What is the smallest positive integer that can not be written as a sum of positive integer powers of distinct elements of {1,…,n}?

score 112 · Answer 11 · 2023-08-21 06:59:02

112

Views

Simply calculate $\frac{ \frac{65536!}{(65536 - 100)! }}{65536^{100}}$

Published on 21 Aug 2023 - 6:59

score 84 · Answer 12 · 2026-03-30 06:47:37

84

Views

How to evaluate the infinite product $\prod_{n\geq1}\prod_{k\geq1}e^{\frac{(-1)^{n+k}}{n^2k^2+3nk^2+3n^2k+2k^2+2n^2+9kn+6k+6n+4}}$

Published on 30 Mar 2026 - 6:47

score 133 · Answer 13 · 2026-04-02 12:59:48

133

Views

How to $a^b \to b^a$

Published on 02 Apr 2026 - 12:59

score 51 · Answer 14 · 2023-09-09 07:25:59

51

Views

About Non-integer Exponentiation and Graphs of Exponential Functions

Published on 09 Sep 2023 - 7:25

score 131 · Answer 15 · 2023-09-12 23:49:23

131

Views

Why is $2^3 = 8$, but $2^{6/2}$ is technically $\pm 8$?

Published on 12 Sep 2023 - 23:49

List Question

Is there any way express $2^{6/x} - 2^{x+1} + 12 = 0$ taking $2^x$ as some variable, say $a$?

Find x and y for $11^x=5*2^y+1$

Solve the equation in integers numbers $3x^2-2xy-7=y^2$.

help me with idea to understand: Determine the real number x for which the value of the expression $E(x)=\sqrt{x^2-4x+5}+\sqrt{x^2-6x+13}$ is minimum

If $a,b,c$ are nonzero natural numbers that verify the relation $a^2+b^2=c^2$, show that $a^n+b^n<c^n$.

Is this a unique property of power functions?

Is there a way to simplify this exponent?

If $a,b,x\in\mathbb{R}^+$ and $a<b$ then $a^x<b^x$

Simplification - Power of diagonal matrix and circulant matrix

What is the smallest positive integer that can not be written as a sum of positive integer powers of distinct elements of {1,…,n}?

Simply calculate $\frac{ \frac{65536!}{(65536 - 100)! }}{65536^{100}}$

How to evaluate the infinite product $\prod_{n\geq1}\prod_{k\geq1}e^{\frac{(-1)^{n+k}}{n^2k^2+3nk^2+3n^2k+2k^2+2n^2+9kn+6k+6n+4}}$

How to $a^b \to b^a$

About Non-integer Exponentiation and Graphs of Exponential Functions

Why is $2^3 = 8$, but $2^{6/2}$ is technically $\pm 8$?

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