List questions from logarithms

Published on 13 Apr 2026 - 19:26

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Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$

Published on 27 Mar 2026 - 18:54

120

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What am I missing in this argument for $\lim\limits_{x\rightarrow \infty} \ln x = \infty$?

Published on 04 May 2026 - 14:53

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How to prove that $\log(x)<x$ when $x>1$?

Published on 15 Apr 2026 - 3:49

878

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Growth rates slower than logarithmic?

Published on 23 Apr 2026 - 11:35

376

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Hyperbolic Cosine: System of Equations, Isolate Variables

Published on 28 Mar 2026 - 20:06

124

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How can a positive integrand integrate to 0?

Published on 25 Mar 2026 - 19:59

83

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Problem with custom made natural log and power functions

Published on 09 Apr 2026 - 12:36

136

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$c= (a^{x}-b^{x})$ where $a$,$b$ and $c$ are known real constants. Solve for $x$.

Published on 15 Apr 2026 - 11:19

65

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If $f(x)=\log \left(\cfrac{1+x}{1-x}\right)$ for $-1 < x < 1$,then find $f \left(\cfrac{3x+x^3}{1+3x^2}\right)$ in terms of $f(x)$.

Published on 15 Apr 2026 - 20:10

8.1k

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Evaluating $\int_{0}^{\pi}\ln (1+\cos x)\, dx$

Published on 15 Apr 2026 - 21:47

344

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Integral $\int_0^{1/2}\arcsin x\cdot\ln^3x\,dx$

Published on 15 Apr 2026 - 5:11

88

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How to derive this simple equality?

Published on 03 Apr 2026 - 0:26

57

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Divergence of $\sum_{n\geq 2} \frac{1}{\ln^p n}$ for $1<p\leq \infty$

Published on 01 Apr 2026 - 22:38

569

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For which values of $a\in\mathbb{R} $ the equation $2 \log(x+3)=\log(ax)$ has exactly one root?

Published on 14 Apr 2026 - 18:12

List Question

What is the $n^{th}$ derivative of $\log_x(e)$?

Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$

What am I missing in this argument for $\lim\limits_{x\rightarrow \infty} \ln x = \infty$?

How to prove that $\log(x)<x$ when $x>1$?

Growth rates slower than logarithmic?

Hyperbolic Cosine: System of Equations, Isolate Variables

How can a positive integrand integrate to 0?

Problem with custom made natural log and power functions

$c= (a^{x}-b^{x})$ where $a$,$b$ and $c$ are known real constants. Solve for $x$.

If $f(x)=\log \left(\cfrac{1+x}{1-x}\right)$ for $-1 < x < 1$,then find $f \left(\cfrac{3x+x^3}{1+3x^2}\right)$ in terms of $f(x)$.

Evaluating $\int_{0}^{\pi}\ln (1+\cos x)\, dx$

Integral $\int_0^{1/2}\arcsin x\cdot\ln^3x\,dx$

How to derive this simple equality?

Divergence of $\sum_{n\geq 2} \frac{1}{\ln^p n}$ for $1<p\leq \infty$

For which values of $a\in\mathbb{R} $ the equation $2 \log(x+3)=\log(ax)$ has exactly one root?

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