List questions from logarithms

Published on 17 Apr 2026 - 3:45

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Find the value of $\log_8 9 \times \log_9 10 \times \cdots \times \log_n(n+1) \times \log_{n+1}8$

Published on 16 Apr 2026 - 4:41

143

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How to prove that $\ln(1+x^2)<x$ , given that $x>0$

Published on 13 Apr 2026 - 21:08

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Understand Logarithm of Bar values manipulation step.

Published on 13 Apr 2026 - 2:20

61

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Let $ f(x)= ( \log_e x) ^2 $ and (Integration by parts. Comparing integrals of different limits )

Published on 14 Apr 2026 - 19:48

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Strange log scale on a plot. How do I read this?

Published on 14 Apr 2026 - 20:13

911

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$N =\sum_{k = 1}^{1000}k(\lceil\log_{\sqrt{2}}k\rceil-\lfloor\log_{\sqrt{2}}k\rfloor). $

Published on 14 Apr 2026 - 23:58

78

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Differentiating this problem $\frac{2t^{3/2}}{\ln(2t^{3/2}+1)}$

Published on 16 Apr 2026 - 13:37

675

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What is the correct integral of $\frac{1}{x}$?

Published on 15 Apr 2026 - 3:04

5.7k

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Show that if $1> x>0$, then $x-1 ≥ \ln(x) ≥ 1−\frac{1}{x}$

Published on 17 Apr 2026 - 1:31

93

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Natural logarithm equation, beginner stage

Published on 08 Apr 2026 - 21:57

1.3k

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Show $\log(1+x)$ is not a contraction mapping

Published on 15 Apr 2026 - 10:00

41

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Minimum of the difference of two logarithms

Published on 17 Apr 2026 - 13:33

913

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Iterative Logarithm in Recurrence Relation?

Published on 10 Apr 2026 - 6:48

94

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Logarithm and trigonometry

Published on 13 Apr 2026 - 10:56

List Question

Domain of $\log\lvert x^3+1\rvert$

Find the value of $\log_8 9 \times \log_9 10 \times \cdots \times \log_n(n+1) \times \log_{n+1}8$

How to prove that $\ln(1+x^2)<x$ , given that $x>0$

Understand Logarithm of Bar values manipulation step.

Let $ f(x)= ( \log_e x) ^2 $ and (Integration by parts. Comparing integrals of different limits )

Strange log scale on a plot. How do I read this?

$N =\sum_{k = 1}^{1000}k(\lceil\log_{\sqrt{2}}k\rceil-\lfloor\log_{\sqrt{2}}k\rfloor). $

Differentiating this problem $\frac{2t^{3/2}}{\ln(2t^{3/2}+1)}$

What is the correct integral of $\frac{1}{x}$?

Show that if $1> x>0$, then $x-1 ≥ \ln(x) ≥ 1−\frac{1}{x}$

Natural logarithm equation, beginner stage

Show $\log(1+x)$ is not a contraction mapping

Minimum of the difference of two logarithms

Iterative Logarithm in Recurrence Relation?

Logarithm and trigonometry

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