List questions from logarithms

Published on 11 May 2026 - 9:15

258

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How to simplify this formula: $ x^{\ln \left( 3 \right)}-3^{\ln \left( x \right)}$?

Published on 13 Apr 2026 - 1:54

59

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Find $x$ in a logarithmic equation

Published on 15 Apr 2026 - 2:34

402

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Simplifying $\log A\cdot\log B$

Published on 16 Apr 2026 - 9:43

250

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Does $2 \log(-1) = 0$?

Published on 10 Apr 2026 - 21:28

44

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Find $x_n$ such that $ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}$

Published on 17 Apr 2026 - 8:17

158

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Why do we have that $ \sqrt{ 1 + \frac{- \log \log n}{\log n} + o(\tfrac{1}{\log n})} = 1 + \frac{- \log \log n}{2\log n} + o(\tfrac{1}{\log n}) $?

Published on 17 Apr 2026 - 15:04

489

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Why is $\ln\frac{1}{x}=-\ln x$?

Published on 16 Apr 2026 - 0:58

85

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Exponential function inequality with n terms

Published on 10 May 2026 - 17:50

6.1k

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How can we come up with the definition of natural logarithm?

Published on 10 May 2026 - 13:50

842

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Comparing $\log_2 3$ to $\log_3 5$

Published on 14 May 2026 - 7:31

176

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Calculate and provide some justification to get an approximation of $\Re(\int_0^1(\log x)^{-\operatorname{li}(x)}dx)$

Published on 15 Apr 2026 - 9:09

38

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A Ln relationship I'm confused

Published on 13 Apr 2026 - 5:50

47

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Solving for $t$ in $t=x^t$

Published on 15 Apr 2026 - 19:42

87

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an inequality involving e.

Published on 11 May 2026 - 5:11

List Question

Find the maximum value of $8\cdot27^{\log_6 x}+27\cdot8^{\log_6 x}-x^3$

How to simplify this formula: $ x^{\ln \left( 3 \right)}-3^{\ln \left( x \right)}$?

Find $x$ in a logarithmic equation

Simplifying $\log A\cdot\log B$

Does $2 \log(-1) = 0$?

Find $x_n$ such that $ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}$

Why do we have that $ \sqrt{ 1 + \frac{- \log \log n}{\log n} + o(\tfrac{1}{\log n})} = 1 + \frac{- \log \log n}{2\log n} + o(\tfrac{1}{\log n}) $?

Why is $\ln\frac{1}{x}=-\ln x$?

Exponential function inequality with n terms

How can we come up with the definition of natural logarithm?

Comparing $\log_2 3$ to $\log_3 5$

Calculate and provide some justification to get an approximation of $\Re(\int_0^1(\log x)^{-\operatorname{li}(x)}dx)$

A Ln relationship I'm confused

Solving for $t$ in $t=x^t$

an inequality involving e.

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