List questions from logarithms

Published on 08 Apr 2026 - 5:42

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Trouble with Logarithmic Differentiation

Published on 17 Jul 2014 - 15:40

505

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A series with only rational terms for $\ln \ln 2$

Published on 17 Jul 2014 - 15:49

82

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Solve x in logarithm equation: $2\log_{10} (x-4) - \log_{10}4(x-1) = 0$

Published on 18 Jul 2014 - 15:08

16.2k

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What is the integral of x/ln(x)?

Published on 18 Jul 2014 - 15:15

9.5k

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Am I allowed to apply L'Hospital's Rule inside of the natural logarithm function?

Published on 19 Jul 2014 - 0:46

85

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What's an intuitive way to compute summation of this series?

Published on 19 Jul 2014 - 12:04

428

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Prove this polylogarithmic integral has the stated closed form value

Published on 26 Mar 2026 - 1:02

373

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Closed form $\sum_{n=2}^{\infty} \frac{1}{\ln^n{n}}$ and $\sum_{n=2}^{\infty} \frac{n}{\ln^n{n}}$

Published on 28 Mar 2026 - 6:59

71

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$e$ and natural logarithms

Published on 21 Jul 2014 - 11:49

465

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$\int_{0}^{\pi/2}\ln\left(1+4\sin^4 x\right)\mathrm{d}x$ and the golden ratio

Published on 25 Mar 2026 - 11:03

853

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A Binet-like integral $\int_{0}^{1} \left(\frac{1}{\ln x} + \frac{1}{1-x} -\frac{1}{2} \right) \frac{x^s }{1-x}\mathrm{d}x$

Published on 21 Jul 2014 - 19:25

137

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$-\varepsilon\log(x)\overset{?}{\geq} -\log(\varepsilon x)$

Published on 21 Jul 2014 - 21:17

206

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Proving $\log(b^a) = a \log(b)$ using calculus

Published on 04 Apr 2026 - 2:25

313

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Proof that $\log(a^b) = b\log a$ when $\log$ is defined by an integral

Published on 21 Jul 2014 - 22:41

List Question

Exponential function to logarithmic function

Trouble with Logarithmic Differentiation

A series with only rational terms for $\ln \ln 2$

Solve x in logarithm equation: $2\log_{10} (x-4) - \log_{10}4(x-1) = 0$

What is the integral of x/ln(x)?

Am I allowed to apply L'Hospital's Rule inside of the natural logarithm function?

What's an intuitive way to compute summation of this series?

Prove this polylogarithmic integral has the stated closed form value

Closed form $\sum_{n=2}^{\infty} \frac{1}{\ln^n{n}}$ and $\sum_{n=2}^{\infty} \frac{n}{\ln^n{n}}$

$e$ and natural logarithms

$\int_{0}^{\pi/2}\ln\left(1+4\sin^4 x\right)\mathrm{d}x$ and the golden ratio

A Binet-like integral $\int_{0}^{1} \left(\frac{1}{\ln x} + \frac{1}{1-x} -\frac{1}{2} \right) \frac{x^s }{1-x}\mathrm{d}x$

$-\varepsilon\log(x)\overset{?}{\geq} -\log(\varepsilon x)$

Proving $\log(b^a) = a \log(b)$ using calculus

Proof that $\log(a^b) = b\log a$ when $\log$ is defined by an integral

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