Question

Challenge: Solve $x^x = \frac{1}{256}$ without the use of the Lambert W function

score 91 · Answer 1 · 2026-04-15 19:04:47

91

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Challenge: Solve $x^x = \frac{1}{256}$ without the use of the Lambert W function

Published on 15 Apr 2026 - 19:04

score 103 · Answer 2 · 2026-04-15 04:53:37

103

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Help me find the logical mistake in this reasoning

Published on 15 Apr 2026 - 4:53

score 97 · Answer 3 · 2026-04-16 03:22:22

97

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Exponential manipulation: is $8^x-2^x=(8 - 2)^x$ valid?

Published on 16 Apr 2026 - 3:22

score 54 · Answer 4 · 2026-04-15 20:52:51

54

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How does $3^{n+1}-3+2\cdot 3^{n+1}$ become $3\cdot 3^{n+1}-3$?

Published on 15 Apr 2026 - 20:52

score 85 · Answer 5 · 2026-04-13 23:24:19

85

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Can $x^{\mathrm{cm}}$ ($x$ to the power $\mathrm{cm}$) be defined?

Published on 13 Apr 2026 - 23:24

score 387 · Answer 6 · 2026-04-14 08:27:34

387

Views

Show that if $A$ and $B$ commute, then $B$ commutes with $e^A$

Published on 14 Apr 2026 - 8:27

score 100 · Answer 7 · 2026-04-21 21:37:17

100

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some cardinal arithmetic

Published on 21 Apr 2026 - 21:37

score 135 · Answer 8 · 2026-04-16 01:26:45

135

Views

Can every number be written as $2^{a_1}+\cdots+2^{a_n} + 1$?

Published on 16 Apr 2026 - 1:26

score 33 · Answer 9 · 2026-04-14 20:50:38

33

Views

When the input to a polynomial is zero and the final term is a constant, why is the evaluation defined or non-zero?

Published on 14 Apr 2026 - 20:50

score 640 · Answer 10 · 2026-04-13 04:42:25

640

Views

Multiclass Classification: Why do we exponentiate the softmax function?

Published on 13 Apr 2026 - 4:42

score 65 · Answer 11 · 2026-04-12 18:48:38

65

Views

Express square root in terms of log 10

Published on 12 Apr 2026 - 18:48

score 73 · Answer 12 · 2026-04-17 00:39:19

73

Views

Find all values of $m$ such that the equation $3^{x^2 + 2mx + 4m - 3} - 2 = \left|\dfrac{m - 2}{x + m}\right|$ has two distinct roots on $[-4; 0]$.

Published on 17 Apr 2026 - 0:39

score 53 · Answer 13 · 2026-04-15 17:43:01

53

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How many integer values of $y$ are there such that there are no more than $2021$ integer values of $x$ wherein $\log_2(x+y^2+1)-3^{y^2+y-3x}<0$?

Published on 15 Apr 2026 - 17:43

score 195 · Answer 14 · 2026-04-16 14:41:30

195

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Is there a name for this function or a concept similar to it?

Published on 16 Apr 2026 - 14:41

score 513 · Answer 15 · 2026-04-15 06:01:05

513

Views

Why $f^2(x) \ne f(x)^2$?

Published on 15 Apr 2026 - 6:01

List Question

Challenge: Solve $x^x = \frac{1}{256}$ without the use of the Lambert W function

Help me find the logical mistake in this reasoning

Exponential manipulation: is $8^x-2^x=(8 - 2)^x$ valid?

How does $3^{n+1}-3+2\cdot 3^{n+1}$ become $3\cdot 3^{n+1}-3$?

Can $x^{\mathrm{cm}}$ ($x$ to the power $\mathrm{cm}$) be defined?

Show that if $A$ and $B$ commute, then $B$ commutes with $e^A$

some cardinal arithmetic

Can every number be written as $2^{a_1}+\cdots+2^{a_n} + 1$?

When the input to a polynomial is zero and the final term is a constant, why is the evaluation defined or non-zero?

Multiclass Classification: Why do we exponentiate the softmax function?

Express square root in terms of log 10

Find all values of $m$ such that the equation $3^{x^2 + 2mx + 4m - 3} - 2 = \left|\dfrac{m - 2}{x + m}\right|$ has two distinct roots on $[-4; 0]$.

How many integer values of $y$ are there such that there are no more than $2021$ integer values of $x$ wherein $\log_2(x+y^2+1)-3^{y^2+y-3x}<0$?

Is there a name for this function or a concept similar to it?

Why $f^2(x) \ne f(x)^2$?

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