Question

Show that $n \log(n!) = n \log n − n + \mathcal{O}(\log n).$

score 95 · Answer 1 · 2026-04-16 22:54:15

95

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Show that $n \log(n!) = n \log n − n + \mathcal{O}(\log n).$

Published on 16 Apr 2026 - 22:54

score 92 · Answer 2 · 2026-04-14 20:39:11

92

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question on Natural Log, $\lim \limits_{n\to∞ }(1+\frac{1}{n} + \frac{1}{n^2})^n $

Published on 14 Apr 2026 - 20:39

score 38 · Answer 3 · 2026-04-12 05:16:50

38

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Verification of a logarithmic inequality

Published on 12 Apr 2026 - 5:16

score 234 · Answer 4 · 2026-04-12 15:35:14

234

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How do I write a super-logarithm in a graphing application such as Desmos?

Published on 12 Apr 2026 - 15:35

score 83 · Answer 5 · 2026-04-16 15:42:41

83

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Evaluating $ \lim_{h\to 0}\frac1h\left(\log(x+h+\sqrt{(x+h)^2+a})-\log(x+\sqrt{x^2+a})\right)$

Published on 16 Apr 2026 - 15:42

score 134 · Answer 6 · 2026-04-14 17:04:44

134

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If we write $\ln(x):=\int_{1}^{x}\frac{1}{t}dt$, can we show that the natural logarithm tells us the power $e$ must be raised to in order to get $x$?

Published on 14 Apr 2026 - 17:04

score 538 · Answer 7 · 2026-04-10 16:53:21

538

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Converting logarithm to decimal form

Published on 10 Apr 2026 - 16:53

score 89 · Answer 8 · 2026-04-14 05:25:50

89

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Calculate $\lim_{R\to \infty} \int_{C_R} e^{iz}/z dz$

Published on 14 Apr 2026 - 5:25

score 67 · Answer 9 · 2026-04-16 20:54:06

67

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Evaluate the integral $\int\limits_{0}^{b}\frac{dx}{\sqrt{a^2+x^2}}$

Published on 16 Apr 2026 - 20:54

score 78 · Answer 10 · 2026-04-16 15:04:05

78

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Show that $\log( x^\alpha + 2)/\log(x + 2)$, $0 < \alpha < 1$, has a unique critical point on $(0, \infty)$

Published on 16 Apr 2026 - 15:04

score 62 · Answer 11 · 2026-03-26 02:52:31

62

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Solving this equation that involves Lambert W function is challenging

Published on 26 Mar 2026 - 2:52

score 64 · Answer 12 · 2026-04-17 01:32:10

64

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Find Solution set of $(\log_4x)^2+4\sqrt{(\log_4x)^2-\log_2x-4}=\log_2x+16$

Published on 17 Apr 2026 - 1:32

score 51 · Answer 13 · 2026-04-08 20:45:50

51

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Logarithm help with order of growth

Published on 08 Apr 2026 - 20:45

score 118 · Answer 14 · 2026-04-16 08:29:45

118

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Taylor series for $\ln(\frac{1-z^2}{1+z^3})$

Published on 16 Apr 2026 - 8:29

score 31 · Answer 15 · 2026-04-09 00:39:57

31

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how to derive the cross enthropy equation from the information theory?

Published on 09 Apr 2026 - 0:39

List Question

Show that $n \log(n!) = n \log n − n + \mathcal{O}(\log n).$

question on Natural Log, $\lim \limits_{n\to∞ }(1+\frac{1}{n} + \frac{1}{n^2})^n $

Verification of a logarithmic inequality

How do I write a super-logarithm in a graphing application such as Desmos?

Evaluating $ \lim_{h\to 0}\frac1h\left(\log(x+h+\sqrt{(x+h)^2+a})-\log(x+\sqrt{x^2+a})\right)$

If we write $\ln(x):=\int_{1}^{x}\frac{1}{t}dt$, can we show that the natural logarithm tells us the power $e$ must be raised to in order to get $x$?

Converting logarithm to decimal form

Calculate $\lim_{R\to \infty} \int_{C_R} e^{iz}/z dz$

Evaluate the integral $\int\limits_{0}^{b}\frac{dx}{\sqrt{a^2+x^2}}$

Show that $\log( x^\alpha + 2)/\log(x + 2)$, $0 < \alpha < 1$, has a unique critical point on $(0, \infty)$

Solving this equation that involves Lambert W function is challenging

Find Solution set of $(\log_4x)^2+4\sqrt{(\log_4x)^2-\log_2x-4}=\log_2x+16$

Logarithm help with order of growth

Taylor series for $\ln(\frac{1-z^2}{1+z^3})$

how to derive the cross enthropy equation from the information theory?

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