Question

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

score 66 · Answer 1 · 2018-02-28 01:35:04

66

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

Published on 28 Feb 2018 - 1:35

score 67 · Answer 2 · 2026-03-25 09:29:49

67

Views

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 25 Mar 2026 - 9:29

score 3.7k · Answer 3 · 2026-03-23 00:43:23

3.7k

Views

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

Published on 23 Mar 2026 - 0:43

score 143 · Answer 4 · 2026-03-28 16:56:53

143

Views

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

Published on 28 Mar 2026 - 16:56

score 350 · Answer 5 · 2026-03-28 10:35:21

350

Views

Proving that a quasi-polynomial grows faster than any polynomial

Published on 28 Mar 2026 - 10:35

score 84 · Answer 6 · 2026-03-27 04:34:43

84

Views

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

Published on 27 Mar 2026 - 4:34

score 70 · Answer 7 · 2018-03-01 06:49:14

70

Views

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

Published on 01 Mar 2018 - 6:49

score 116 · Answer 8 · 2026-03-20 09:47:53

116

Views

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

Published on 20 Mar 2026 - 9:47

score 44 · Answer 9 · 2026-03-26 16:05:08

44

Views

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

Published on 26 Mar 2026 - 16:05

score 56 · Answer 10 · 2026-03-24 23:41:05

56

Views

Compacting a number scale using a logarithmic function

Published on 24 Mar 2026 - 23:41

score 799 · Answer 11 · 2026-03-26 14:13:34

799

Views

Mercator projection - Use existing equation to solve for degrees

Published on 26 Mar 2026 - 14:13

score 315 · Answer 12 · 2026-03-25 15:41:08

315

Views

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

Published on 25 Mar 2026 - 15:41

score 82 · Answer 13 · 2026-03-25 04:42:50

82

Views

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

Published on 25 Mar 2026 - 4:42

score 1.2k · Answer 14 · 2026-03-25 09:23:20

1.2k

Views

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

Published on 25 Mar 2026 - 9:23

score 256 · Answer 15 · 2026-03-25 20:59:54

256

Views

How do you deal with logs with multiple bases?

Published on 25 Mar 2026 - 20:59

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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