Question

Find sum $ \sum\limits_{k=2}^{2^{2^n}} \frac{1}{2^{\lfloor \log_2k \rfloor} \cdot 4^{\lfloor \log_2(\log_2k )\rfloor}} $

score 159 · Answer 1 · 2026-03-26 11:01:34

159

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Find sum $ \sum\limits_{k=2}^{2^{2^n}} \frac{1}{2^{\lfloor \log_2k \rfloor} \cdot 4^{\lfloor \log_2(\log_2k )\rfloor}} $

Published on 26 Mar 2026 - 11:01

score 109 · Answer 2 · 2019-03-10 00:25:41

109

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Find the sum $\sum_{n=1}^{\infty} (-1)^{n-1}\log \left(1- \frac{1}{(n+1)^2}\right)$ based on $a^2-b^2 $?

Published on 10 Mar 2019 - 0:25

score 36 · Answer 3 · 2019-03-10 07:32:55

36

Views

Proving an inequality involving logarithm

Published on 10 Mar 2019 - 7:32

score 117 · Answer 4 · 2019-03-10 07:41:45

117

Views

What am I doing wrong calculating natural logarithm of this matrix?

Published on 10 Mar 2019 - 7:41

score 1.9k · Answer 5 · 2019-03-10 18:37:39

1.9k

Views

How do we get from $\ln A=\ln P+rn$ to $A=Pe^{rn}$ and similar logarithmic equations?

Published on 10 Mar 2019 - 18:37

score 81 · Answer 6 · 2026-03-25 01:33:05

81

Views

Finding expression for variable x from equations like xlogx + y = 0

Published on 25 Mar 2026 - 1:33

score 85 · Answer 7 · 2019-03-11 01:53:11

85

Views

Proving an inequality with logs and L'Hopital Rule

Published on 11 Mar 2019 - 1:53

score 101 · Answer 8 · 2019-03-11 03:47:24

101

Views

Help with $\frac12 \log_2 x - \frac1{\log_2 x} = \frac76$

Published on 11 Mar 2019 - 3:47

score 562 · Answer 9 · 2019-03-11 10:20:52

562

Views

Proving $\int_0^\infty \log\left (1-2\frac{\cos 2\theta}{x^2}+\frac{1}{x^4} \right)dx =2\pi \sin \theta$

Published on 11 Mar 2019 - 10:20

score 393 · Answer 10 · 2026-03-27 21:23:05

393

Views

How did I solve this (triply logarithmic) equation?

Published on 27 Mar 2026 - 21:23

score 56 · Answer 11 · 2026-03-25 01:31:26

56

Views

Finding expression for variable x in an equation (use Lambert function?)

Published on 25 Mar 2026 - 1:31

score 69 · Answer 12 · 2019-03-11 15:15:19

69

Views

A simpler method to prove $\log_{b}{a} \times \log_{c}{b} \times \log_{a}{c} = 1?$

Published on 11 Mar 2019 - 15:15

score 46 · Answer 13 · 2019-03-11 18:52:38

46

Views

GCSE logarithmic problem - don't know base

Published on 11 Mar 2019 - 18:52

score 442 · Answer 14 · 2019-03-11 20:42:58

442

Views

derivative of log(y) function.

Published on 11 Mar 2019 - 20:42

score 39 · Answer 15 · 2019-03-11 22:43:20

39

Views

Determining the value of n in inequality with logs

Published on 11 Mar 2019 - 22:43

List Question

Find sum $ \sum\limits_{k=2}^{2^{2^n}} \frac{1}{2^{\lfloor \log_2k \rfloor} \cdot 4^{\lfloor \log_2(\log_2k )\rfloor}} $

Find the sum $\sum_{n=1}^{\infty} (-1)^{n-1}\log \left(1- \frac{1}{(n+1)^2}\right)$ based on $a^2-b^2 $?

Proving an inequality involving logarithm

What am I doing wrong calculating natural logarithm of this matrix?

How do we get from $\ln A=\ln P+rn$ to $A=Pe^{rn}$ and similar logarithmic equations?

Finding expression for variable x from equations like xlogx + y = 0

Proving an inequality with logs and L'Hopital Rule

Help with $\frac12 \log_2 x - \frac1{\log_2 x} = \frac76$

Proving $\int_0^\infty \log\left (1-2\frac{\cos 2\theta}{x^2}+\frac{1}{x^4} \right)dx =2\pi \sin \theta$

How did I solve this (triply logarithmic) equation?

Finding expression for variable x in an equation (use Lambert function?)

A simpler method to prove $\log_{b}{a} \times \log_{c}{b} \times \log_{a}{c} = 1?$

GCSE logarithmic problem - don't know base

derivative of log(y) function.

Determining the value of n in inequality with logs

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