Question

Simplify $\frac14\log(3x+1)+\frac12\log(x-3)-\frac12\log(x^4-x^2-10)$

score 68 · Answer 1 · 2026-04-17 14:50:06

68

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Simplify $\frac14\log(3x+1)+\frac12\log(x-3)-\frac12\log(x^4-x^2-10)$

Published on 17 Apr 2026 - 14:50

score 71 · Answer 2 · 2026-05-11 09:15:12

71

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Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

Published on 11 May 2026 - 9:15

score 3.7k · Answer 3 · 2026-05-10 12:46:05

3.7k

Views

log(A/B) = log(A)-log(B), where A and B have units

Published on 10 May 2026 - 12:46

score 146 · Answer 4 · 2026-05-14 11:38:19

146

Views

Proof $\frac{\log(n!)}{n\log n}$ is increasing for positive integer $n$ ($\log n=\ln(n)$)

Published on 14 May 2026 - 11:38

score 352 · Answer 5 · 2026-04-13 17:30:16

352

Views

Proving that a quasi-polynomial grows faster than any polynomial

Published on 13 Apr 2026 - 17:30

score 88 · Answer 6 · 2026-05-10 20:55:55

88

Views

Solving $4^{32^x} = 16^{8^x}$

Published on 10 May 2026 - 20:55

score 73 · Answer 7 · 2026-04-16 11:34:23

73

Views

How many solutions are possible for $\log_4 (x-1) = \log_2 (x-3)$?

Published on 16 Apr 2026 - 11:34

score 124 · Answer 8 · 2026-05-12 00:55:54

124

Views

What is this "logarithmic golden ratio of scale-free networks" really called?

Published on 12 May 2026 - 0:55

score 46 · Answer 9 · 2026-04-16 07:02:31

46

Views

Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

Published on 16 Apr 2026 - 7:02

score 59 · Answer 10 · 2026-05-10 13:44:56

59

Views

Compacting a number scale using a logarithmic function

Published on 10 May 2026 - 13:44

score 804 · Answer 11 · 2026-05-11 06:58:56

804

Views

Mercator projection - Use existing equation to solve for degrees

Published on 11 May 2026 - 6:58

score 317 · Answer 12 · 2026-04-15 14:47:41

317

Views

Why is $\ln (\ln (n) - \ln (\ln (n)))$ asymptotically $\ln( \ln (n))$?

Published on 15 Apr 2026 - 14:47

score 85 · Answer 13 · 2026-05-10 17:01:52

85

Views

Analytic $f : f(z^5) = 5 \cdot f(z) $ for $0 < arg(z) < \pi / 100$

Published on 10 May 2026 - 17:01

score 1.2k · Answer 14 · 2026-05-11 06:28:47

1.2k

Views

Prove $a^{\log_bc}=c^{\log_ba}$

Published on 11 May 2026 - 6:28

score 259 · Answer 15 · 2026-05-11 03:46:57

259

Views

How do you deal with logs with multiple bases?

Published on 11 May 2026 - 3:46

List Question

Simplify $\frac14\log(3x+1)+\frac12\log(x-3)-\frac12\log(x^4-x^2-10)$

Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

log(A/B) = log(A)-log(B), where A and B have units

Proof $\frac{\log(n!)}{n\log n}$ is increasing for positive integer $n$ ($\log n=\ln(n)$)

Proving that a quasi-polynomial grows faster than any polynomial

Solving $4^{32^x} = 16^{8^x}$

How many solutions are possible for $\log_4 (x-1) = \log_2 (x-3)$?

What is this "logarithmic golden ratio of scale-free networks" really called?

Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

Compacting a number scale using a logarithmic function

Mercator projection - Use existing equation to solve for degrees

Why is $\ln (\ln (n) - \ln (\ln (n)))$ asymptotically $\ln( \ln (n))$?

Analytic $f : f(z^5) = 5 \cdot f(z) $ for $0 < arg(z) < \pi / 100$

Prove $a^{\log_bc}=c^{\log_ba}$

How do you deal with logs with multiple bases?

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