List questions from logarithms

Published on 14 Apr 2026 - 21:28

195

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How can I solve $\int_{0}^{\infty}{\frac{\log(x)}{x^2+4}}dx$ using $2\tan\theta$ as substitution for x?

Published on 16 Apr 2026 - 15:34

63

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A value from which a positive power of x beats a logarithm

Published on 12 Apr 2026 - 7:52

136

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Prove that $\tanh (\cosh^{-1} (x)) = \frac{\sqrt{x^2-1}}{x}$

Published on 16 Apr 2026 - 13:18

57

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Bounding a difference by the logarithm of a fraction

Published on 15 Apr 2026 - 7:28

72

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How to solve $x^x = n$ algebraically?

Published on 13 Apr 2026 - 18:58

24

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coniditons for integrability for log(X) where X is a r.v.?

Published on 14 Apr 2026 - 3:12

198

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find the asymptotic bound of $T(n-1) + n/\log n$

Published on 16 Apr 2026 - 10:48

50

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Trying to understand a proof

Published on 10 Apr 2026 - 21:06

81

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Which base to use when taking log of both sides in an inequality?

Published on 12 Apr 2026 - 8:46

145

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How do we evaluate this integral containing log

Published on 15 Apr 2026 - 20:52

95

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Why is $\frac{\log(y)}{\log(x)} = \log_{x}(y)$?

Published on 16 Apr 2026 - 21:31

59

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Why $e^{y \log(p)} = p^y$

Published on 14 Apr 2026 - 3:19

125

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Approximation of $\frac1x\sum_{k=0}^n\frac{e^{-k^2x}-e^{-(k+1)^2x}}{2k+1}$

Published on 15 Apr 2026 - 4:14

885

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How to prove that $\log_5(6)>\log_6(7)$?

Published on 25 Mar 2026 - 7:43

List Question

Asymptotic behavior of sequence

How can I solve $\int_{0}^{\infty}{\frac{\log(x)}{x^2+4}}dx$ using $2\tan\theta$ as substitution for x?

A value from which a positive power of x beats a logarithm

Prove that $\tanh (\cosh^{-1} (x)) = \frac{\sqrt{x^2-1}}{x}$

Bounding a difference by the logarithm of a fraction

How to solve $x^x = n$ algebraically?

coniditons for integrability for log(X) where X is a r.v.?

find the asymptotic bound of $T(n-1) + n/\log n$

Trying to understand a proof

Which base to use when taking log of both sides in an inequality?

How do we evaluate this integral containing log

Why is $\frac{\log(y)}{\log(x)} = \log_{x}(y)$?

Why $e^{y \log(p)} = p^y$

Approximation of $\frac1x\sum_{k=0}^n\frac{e^{-k^2x}-e^{-(k+1)^2x}}{2k+1}$

How to prove that $\log_5(6)>\log_6(7)$?

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