From 746f76296dbeb7136509af350759a8d268adc6c4 Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Wed, 7 Dec 2022 11:29:17 +0100 Subject: [PATCH 1/3] vault backup: 2022-12-07 11:29:17 --- .../obsidian-activity-history/data.json | 10 +- notes/.obsidian/workspace.json | 24 ++-- notes/mat/Funkce/Logaritmus.md | 115 +++++++++++++++++- 3 files changed, 133 insertions(+), 16 deletions(-) diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index 16fc13d..bafe212 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -12,8 +12,8 @@ "checkpointList": [ { "path": "/", - "date": "2022-12-06", - "size": 948992 + "date": "2022-12-07", + "size": 950468 } ], "activityHistory": [ @@ -954,7 +954,11 @@ }, { "date": "2022-12-06", - "value": 1215 + "value": 2182 + }, + { + "date": "2022-12-07", + "value": 509 } ] } diff --git a/notes/.obsidian/workspace.json b/notes/.obsidian/workspace.json index ecc5546..9004b23 100644 --- a/notes/.obsidian/workspace.json +++ b/notes/.obsidian/workspace.json @@ -13,7 +13,7 @@ "state": { "type": "markdown", "state": { - "file": "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md", + "file": "mat/Funkce/Logaritmus.md", "mode": "source", "source": false } @@ -77,7 +77,7 @@ "state": { "type": "backlink", "state": { - "file": "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md", + "file": "mat/Funkce/Logaritmus.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -94,7 +94,7 @@ "state": { "type": "outgoing-link", "state": { - "file": "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md", + "file": "mat/Funkce/Logaritmus.md", "linksCollapsed": false, "unlinkedCollapsed": true } @@ -141,7 +141,7 @@ "state": { "type": "outline", "state": { - "file": "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md" + "file": "mat/Funkce/Logaritmus.md" } } }, @@ -203,15 +203,15 @@ }, "active": "f7d9932211c6b72c", "lastOpenFiles": [ + "mat/mat.md", + "dej/dej.md", + "dej/moderní/komunismus/Brutalismus.md", + "dej/moderní/komunismus/České století, Všechnu moc lidu Stalinovi.md", + "mat/Funkce/Logaritmus.md", + "fyz/fyz.md", + "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md", "fyz/Mechanika tekutin/Termodynamika/Termodynamika.md", "fyz/Mechanika tekutin/Proudění/Rozdělení.md", - "fyz/Mechanika tekutin/Termodynamika/Celsiova teplotní stupnice.md", - "fyz/Mechanika tekutin/Termodynamika/Termodynamická teplota.md", - "fyz/Mechanika tekutin/Proudění/Proudění.md", - "fyz/Mechanika tekutin/Proudění/Hmotnostní tok.md", - "fyz/Mechanika tekutin/Proudění/Bernoulliho rovnice.md", - "fyz/Mechanika tekutin/Proudění/Proudnice.md", - "har/har.md", - "har/Tiskárny.md" + "fyz/Mechanika tekutin/Termodynamika/Celsiova teplotní stupnice.md" ] } \ No newline at end of file diff --git a/notes/mat/Funkce/Logaritmus.md b/notes/mat/Funkce/Logaritmus.md index 62a665b..be71911 100644 --- a/notes/mat/Funkce/Logaritmus.md +++ b/notes/mat/Funkce/Logaritmus.md @@ -6,6 +6,9 @@ tags: [mat, mat/funkce] Na kalkulačce je log $= log_{10}x$ ln $= log_ex$ +$\log\frac{a}b=\log a - \log b$ +$\log a^2=2\log a$ + $$ \log_ab=x @@ -109,4 +112,114 @@ $a^4=81$ $a^4=3^4$ $a=3$ -$log_a8=-3$ \ No newline at end of file +$log_a8=-3$ + +--- + +$l=log^3\sqrt{\frac{a}b}=\frac{\log a}3-\frac{\log b}3$ +$l=\log^3\sqrt\frac{a}b=\log(\frac{a}b)^\frac13=\frac13\log\frac{a}b=\frac13(\log a - \log b)=\frac{\log a}3-\frac{\log b}3$ + +--- + +$4\log_63+5\log_62-\log_612=v$ +$\log_63^4+\log_62^5-\log_612=v$ +$log_6(\frac{3^4*2^5}{12})=v$ +$\log_6(\frac{3^4*2^5}{3*4})=v$ +$\log_6(\frac{3^3*2^5}{2^2})=v$ +$\log_6(3^3*2^3)=v$ +$\log_6(3^3*2^3)=v$ +$\log_6(6^3)=v$ +$v=3$ + +--- + +$\log_{10}20+\log_{10}50=v$ +$log_{10}(20*50)=v$ +$log_{10}(1000)=v$ +$v=3$ + +--- + +$\log_550-\log_52=v$ +$\log_5(50/2)=v$ +$\log_5(25)=v$ +$\log_5(5^2)=v$ +$v=2$ + +--- + +$\log_37+\log_3\frac{81}7=v$ +$\log_3(7*81/7)=v$ +$\log_3(81)=v$ +$log_3(9^2)=v$ +$log_3({3^2}^2)=v$ +$v=4$ + +--- + +$\log_28-4\log_22+\log_232=v$ +$\log_28-\log_22^4+\log_232=v$ +$\log_2(2^3*2^5/2^4)=v$ +$\log_2(2^8/2^4)=v$ +$\log_2(2^4)=v$ +$v=4$ + +--- + +### Definiční obory +$y=\log(x+3)$ + +$x+3>0$ +$x>-3$ +$D=(-3, \infty)$ + +--- +$y=\log_3(x^2+4x-5)$ + +$x^2+4x-5>0$ + +$x>1$ + +$D=(-\infty;-5)\cup(1; \infty)$ + +--- + +$y=\log_5(8-x)-\log_5(x+5)$ + +$8-x>0$ +$x+5>0$ + +$-x>-8$ +$x<8$ + +$x>-5$ + +$D=(-\infty;8)\cap(-5;\infty)$ +$D=(-5;8)$ + +--- + +$y=\log_\frac35(4-x^2)$ +$y=\log_3(4-x^2)/\log_5(4-x^2)$ + +$4-x^2>0$ +$-x^2>-4$ +$x^2<4$ +$x^2<2^2$ +$x<2$ + +$D=(\infty;2)$ + +--- + +$y=\log_7\sqrt{3+x}$ + +$3+x\le0$ +$x\le-3$ +$x\in\langle-3;\infty)$ + +$\log\sqrt{3+x}>0$ + +$\sqrt{3+x}=0 \Leftrightarrow 3+x=0$ + $x=-3$ + From 67dbd633ed34ddb1c70cd13a1f09add3b20907cf Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Wed, 7 Dec 2022 11:33:36 +0100 Subject: [PATCH 2/3] vault backup: 2022-12-07 11:33:36 --- notes/mat/Funkce/Logaritmus.md | 10 ++++++++++ notes/notes.md | 1 + 2 files changed, 11 insertions(+) diff --git a/notes/mat/Funkce/Logaritmus.md b/notes/mat/Funkce/Logaritmus.md index be71911..1ea8252 100644 --- a/notes/mat/Funkce/Logaritmus.md +++ b/notes/mat/Funkce/Logaritmus.md @@ -223,3 +223,13 @@ $\log\sqrt{3+x}>0$ $\sqrt{3+x}=0 \Leftrightarrow 3+x=0$ $x=-3$ +$D=(-3;\infty)$ + +--- + +$y=\frac1{\log x-1}$ + +$\log x$ +$x\in\mathbb{R}^+$ + +$\log x-1\ne0$ diff --git a/notes/notes.md b/notes/notes.md index ae81298..5a374d3 100644 --- a/notes/notes.md +++ b/notes/notes.md @@ -1,6 +1,7 @@ %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[ang/ang|ang]] - [[cjl/cjl|cjl]] +- [[conflict-files-obsidian-git|conflict-files-obsidian-git]] - [[data/data|data]] - [[dej/dej|dej]] - [[ech/ech|ech]] From 7f7a984f3d1b06ab09ff2c74d698f29bf657902c Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Wed, 7 Dec 2022 11:34:50 +0100 Subject: [PATCH 3/3] vault backup: 2022-12-07 11:34:50 --- notes/.obsidian/workspace.json | 12 ------------ notes/mat/Funkce/Logaritmus.md | 6 ++++++ notes/notes.md | 1 - 3 files changed, 6 insertions(+), 13 deletions(-) diff --git a/notes/.obsidian/workspace.json b/notes/.obsidian/workspace.json index b54c2b0..00d5e9f 100644 --- a/notes/.obsidian/workspace.json +++ b/notes/.obsidian/workspace.json @@ -18,18 +18,6 @@ "source": false } } - }, - { - "id": "2861e7a497039037", - "type": "leaf", - "state": { - "type": "markdown", - "state": { - "file": "conflict-files-obsidian-git.md", - "mode": "source", - "source": false - } - } } ] } diff --git a/notes/mat/Funkce/Logaritmus.md b/notes/mat/Funkce/Logaritmus.md index 1ea8252..6f13077 100644 --- a/notes/mat/Funkce/Logaritmus.md +++ b/notes/mat/Funkce/Logaritmus.md @@ -233,3 +233,9 @@ $\log x$ $x\in\mathbb{R}^+$ $\log x-1\ne0$ + +$\log x -1=0$ +$\log x=1$ +$x=10$ + +$D=\mathbb{R}^+\backslash\{10\}$ diff --git a/notes/notes.md b/notes/notes.md index 5a374d3..ae81298 100644 --- a/notes/notes.md +++ b/notes/notes.md @@ -1,7 +1,6 @@ %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[ang/ang|ang]] - [[cjl/cjl|cjl]] -- [[conflict-files-obsidian-git|conflict-files-obsidian-git]] - [[data/data|data]] - [[dej/dej|dej]] - [[ech/ech|ech]]