List questions from logarithms

Published on 25 Mar 2026 - 11:08

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Prove or disprove that $f(x)\leq 0$

Published on 17 Apr 2026 - 6:14

58

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Usefulness of substitution $x\mapsto\ln x$

Published on 16 Apr 2026 - 4:46

150

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Prove that for all positive integers x that $\lceil \log_{3}(x)\rceil \leq \lfloor \log_{2}(x) \rfloor$

Published on 16 Apr 2026 - 4:40

596

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Evaluation of $\int_0^1\frac{\log x\,dx}{\sqrt{x(1-x)(1-cx)}}$

Published on 26 Mar 2026 - 4:53

131

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Prove $\lim \limits_{h \to 0} \frac{a^h-1}{h} = \ln (a)$ without using L'hospital's.

Published on 15 Apr 2026 - 1:33

79

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How do you show that branch cuts result in a single valued function for logarithmic branch points?

Published on 25 Mar 2026 - 6:34

88

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Hard Logarithm Problem: $\left(\log _{10}\left(x\right)\right)^{\log _{10}\left(\log _{10}\left(x\right)\right)} = 10000$

Published on 17 Apr 2026 - 4:04

78

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Find the least value of $\log_a{bc}+\log_bac+\log_cab$

Published on 17 Apr 2026 - 11:07

73

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Why does $∫{\frac{1+\log x}x}\,\mathrm dx$ not equal $\log x + \frac{(\log x)^2}2 + C?$

Published on 16 Apr 2026 - 19:26

171

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Prove that $\ln(i) = i(\frac{\pi}{2})$

Published on 17 Apr 2026 - 13:45

157

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Solving $|x-1|^{\log_2(4-x)} \le|x-1|^{\log_2 (1+x)}$

Published on 22 Apr 2026 - 9:08

79

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Can someone help me solve for x and y

Published on 14 Apr 2026 - 10:57

45

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Logarithmic rules

Published on 10 Apr 2026 - 7:08

138

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Integral involving $\log(x+a)$

Published on 10 Apr 2026 - 5:50

List Question

Solving for the quantile of a probability density function.

Prove or disprove that $f(x)\leq 0$

Usefulness of substitution $x\mapsto\ln x$

Prove that for all positive integers x that $\lceil \log_{3}(x)\rceil \leq \lfloor \log_{2}(x) \rfloor$

Evaluation of $\int_0^1\frac{\log x\,dx}{\sqrt{x(1-x)(1-cx)}}$

Prove $\lim \limits_{h \to 0} \frac{a^h-1}{h} = \ln (a)$ without using L'hospital's.

How do you show that branch cuts result in a single valued function for logarithmic branch points?

Hard Logarithm Problem: $\left(\log _{10}\left(x\right)\right)^{\log _{10}\left(\log _{10}\left(x\right)\right)} = 10000$

Find the least value of $\log_a{bc}+\log_bac+\log_cab$

Why does $∫{\frac{1+\log x}x}\,\mathrm dx$ not equal $\log x + \frac{(\log x)^2}2 + C?$

Prove that $\ln(i) = i(\frac{\pi}{2})$

Solving $|x-1|^{\log_2(4-x)} \le|x-1|^{\log_2 (1+x)}$

Can someone help me solve for x and y

Logarithmic rules

Integral involving $\log(x+a)$

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