Question

Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$?

score 551 · Answer 1 · 2026-03-24 23:48:11

551

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Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$?

Published on 24 Mar 2026 - 23:48

score 146 · Answer 2 · 2026-03-25 11:27:18

146

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How do I give a good estimate for $3^{3.8}$ or $3^{308}$ or $3^{3.7}$ etc. quickly and without a calculator?

Published on 25 Mar 2026 - 11:27

score 396 · Answer 3 · 2026-03-25 11:25:58

396

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How to calculate non-exact Log problems like: Base 2 Log 10 = 3.32192809489?

Published on 25 Mar 2026 - 11:25

score 101 · Answer 4 · 2026-03-27 00:54:51

101

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Simplify $\log_e(1-e^{a+bt})$

Published on 27 Mar 2026 - 0:54

score 688 · Answer 5 · 2026-03-25 11:06:20

688

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Prove that $x^{18} = y^{21} = z^{28}$

Published on 25 Mar 2026 - 11:06

score 104 · Answer 6 · 2018-05-25 02:00:09

104

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Creating the equation of a logarithmic graph given an asymptote and two intercepts

Published on 25 May 2018 - 2:00

score 163 · Answer 7 · 2026-03-25 10:24:03

163

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Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Published on 25 Mar 2026 - 10:24

score 62 · Answer 8 · 2018-05-25 12:46:58

62

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How do I solve $ n\int_R^{2R} dx/x = 2\int_{R/4}^R dx/x $?

Published on 25 May 2018 - 12:46

score 483 · Answer 9 · 2018-05-25 13:43:17

483

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Solve $\log_3(1/\sqrt{\log_3(x)})=\log_9(\log_9(x/3))$

Published on 25 May 2018 - 13:43

score 508 · Answer 10 · 2026-03-25 20:15:52

508

Views

Using concavity of log to prove $L^p$ norm is increasing in $p$

Published on 25 Mar 2026 - 20:15

score 789 · Answer 11 · 2018-05-25 17:22:15

789

Views

Logarithmic equation $\log_{3x}(3/x)+(\log_3(x))^2=1$.

Published on 25 May 2018 - 17:22

score 362 · Answer 12 · 2026-03-24 19:01:25

362

Views

Solve $x+\log(x-1)\cdot (1-x) = 0$

Published on 24 Mar 2026 - 19:01

score 132 · Answer 13 · 2026-03-30 08:33:00

132

Views

Explanation of proof derivative of logarithms

Published on 30 Mar 2026 - 8:33

score 119 · Answer 14 · 2026-03-26 06:27:44

119

Views

Solve the equation $(6-x)^x=x^{6-x}$

Published on 26 Mar 2026 - 6:27

score 237 · Answer 15 · 2026-03-27 03:29:00

237

Views

Complex analysis - branch cut of log

Published on 27 Mar 2026 - 3:29

List Question

Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$?

How do I give a good estimate for $3^{3.8}$ or $3^{308}$ or $3^{3.7}$ etc. quickly and without a calculator?

How to calculate non-exact Log problems like: Base 2 Log 10 = 3.32192809489?

Simplify $\log_e(1-e^{a+bt})$

Prove that $x^{18} = y^{21} = z^{28}$

Creating the equation of a logarithmic graph given an asymptote and two intercepts

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

How do I solve $ n\int_R^{2R} dx/x = 2\int_{R/4}^R dx/x $?

Solve $\log_3(1/\sqrt{\log_3(x)})=\log_9(\log_9(x/3))$

Using concavity of log to prove $L^p$ norm is increasing in $p$

Logarithmic equation $\log_{3x}(3/x)+(\log_3(x))^2=1$.

Solve $x+\log(x-1)\cdot (1-x) = 0$

Explanation of proof derivative of logarithms

Solve the equation $(6-x)^x=x^{6-x}$

Complex analysis - branch cut of log

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