List questions from logarithms

57

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Given the inequalities $n > 2^k - 1$ and $n < 2^{(k+1)}$, express $k$ in terms of $n$ (where $k, n \in\Bbb N$).

Published on 11 Apr 2026 - 21:55

59

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stuck on this integration problem

Published on 09 Apr 2026 - 9:29

87

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But is there another solution for $i^i=x^x$?

Published on 14 Apr 2026 - 12:03

64

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Branch cut of $\sqrt{z^2 -1}$

Published on 25 Mar 2026 - 16:13

72

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Solving for $x$ in $x^{\ln(x)}=ex$

Published on 16 Apr 2026 - 15:48

36

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How to square a logarithmic expression?

Published on 09 Apr 2026 - 6:02

100

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How does one prove (log(n))^2 is O(n)?

Published on 25 Apr 2026 - 0:10

142

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Which function is eventually larger: $\ln(x)\text{ or }\sqrt[3]x$?

Published on 15 Apr 2026 - 16:46

117

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But will $(\tan(x))^{\ln(\sin(x))}$ ever equal $(\ln(\cot(x)))^{\cos(x)}$

Published on 15 Apr 2026 - 18:58

20

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Squaring the argument of a logarithm with parentheses

Published on 14 Apr 2026 - 22:45

54

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Substitution of $x=\ln y$

Published on 15 Apr 2026 - 13:40

49

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Logarithm product inequality - Where is the Mistake?

Published on 10 Apr 2026 - 3:20

122

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Prove that $\pi=2i\ln\left(\frac{1-i}{1+i}\right)$

Published on 17 Apr 2026 - 18:50

120

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Showing that $\ln(x)^2+2(x-1)\ln x-3x+1=0$ has only $2$ real solutions

Published on 17 Apr 2026 - 10:02

16

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Question being a mixture of algebraic laws and basic properties of logarithm

Published on 12 Apr 2026 - 4:45

List Question

Given the inequalities $n > 2^k - 1$ and $n < 2^{(k+1)}$, express $k$ in terms of $n$ (where $k, n \in\Bbb N$).

stuck on this integration problem

But is there another solution for $i^i=x^x$?

Branch cut of $\sqrt{z^2 -1}$

Solving for $x$ in $x^{\ln(x)}=ex$

How to square a logarithmic expression?

How does one prove (log(n))^2 is O(n)?

Which function is eventually larger: $\ln(x)\text{ or }\sqrt[3]x$?

But will $(\tan(x))^{\ln(\sin(x))}$ ever equal $(\ln(\cot(x)))^{\cos(x)}$

Squaring the argument of a logarithm with parentheses

Substitution of $x=\ln y$

Logarithm product inequality - Where is the Mistake?

Prove that $\pi=2i\ln\left(\frac{1-i}{1+i}\right)$

Showing that $\ln(x)^2+2(x-1)\ln x-3x+1=0$ has only $2$ real solutions

Question being a mixture of algebraic laws and basic properties of logarithm

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