List questions from logarithms

Published on 10 Apr 2026 - 16:10

63

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How to solve $\lim_{x\rightarrow \infty }\dfrac {2} {x}\sum _{k\rightarrow 1}^{x}\ln \left( \dfrac {x+k} {x}\right)$?

Published on 16 Apr 2026 - 2:20

95

Views

Prove that $\log{\frac{\sum_{j=1}^n x_j}{n}}\ge \frac{\sum_{j=1}^n \log x_j}n$ for $j=1,...,n$

Published on 15 Apr 2026 - 11:41

204

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Positive logarithm in a $C^*$-algebra

Published on 29 Mar 2026 - 14:18

85

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Logarithm rule for branch cut logarithms

Published on 26 Mar 2026 - 7:41

215

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Solve the equation: $2^{2x+1}=\left(\frac{1}{32}\right)^x$

Published on 09 Apr 2026 - 9:10

1.4k

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Unitary matrix in trace and log function

Published on 13 Apr 2026 - 14:45

457

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Derivatives and Integrals of Polynomials and more.

Published on 11 Apr 2026 - 19:57

91

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Calculus - limit of a function with logarithms

Published on 12 Apr 2026 - 7:10

35

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Solving for n. Logarithm

Published on 14 Apr 2026 - 6:14

676

Views

Inequality $\log x\le \frac{2}{e} \, \sqrt{x}$

Published on 16 Apr 2026 - 4:36

8k

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Finding the logarithm of a matrix?

Published on 12 Apr 2026 - 17:02

241

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Inequality for Difference Between Two Harmonic Numbers

Published on 29 Mar 2026 - 14:27

497

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Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

Published on 16 May 2026 - 0:34

51

Views

Simplifying a log function

Published on 17 Apr 2026 - 7:57

List Question

In Need of Logarithms Simplification Exercises

How to solve $\lim_{x\rightarrow \infty }\dfrac {2} {x}\sum _{k\rightarrow 1}^{x}\ln \left( \dfrac {x+k} {x}\right)$?

Prove that $\log{\frac{\sum_{j=1}^n x_j}{n}}\ge \frac{\sum_{j=1}^n \log x_j}n$ for $j=1,...,n$

Positive logarithm in a $C^*$-algebra

Logarithm rule for branch cut logarithms

Solve the equation: $2^{2x+1}=\left(\frac{1}{32}\right)^x$

Unitary matrix in trace and log function

Derivatives and Integrals of Polynomials and more.

Calculus - limit of a function with logarithms

Solving for n. Logarithm

Inequality $\log x\le \frac{2}{e} \, \sqrt{x}$

Finding the logarithm of a matrix?

Inequality for Difference Between Two Harmonic Numbers

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

Simplifying a log function

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