diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index 73e7dad..6644642 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -13,7 +13,7 @@ { "path": "/", "date": "2022-10-11", - "size": 916496 + "size": 917393 } ], "activityHistory": [ @@ -858,7 +858,7 @@ }, { "date": "2022-10-11", - "value": 960 + "value": 1857 } ] } diff --git a/notes/mat/Funkce/Exponenciální funkce.md b/notes/mat/Funkce/Exponenciální funkce.md index ec28545..d794e38 100644 --- a/notes/mat/Funkce/Exponenciální funkce.md +++ b/notes/mat/Funkce/Exponenciální funkce.md @@ -160,3 +160,62 @@ $\frac{27^x3^2\sqrt3}{g^x}=1$ --- $\sqrt[5]{(\frac43)^{1-x}}=(\frac34)^{x+3}$ + +$(\frac43)^{\frac{1-x}5}=(\frac43)^{-x+3}$ +$\frac{1-x}5=-x-3$ +$1-x=-5x-15$ +$1=-4x-15$ +$16=-4x$ +$x=-4$ + +$K=\{-4\}$ + +--- + +$0.4^{2x}*2.5=(\frac25)^{x+4}$ + +$(\frac25)^{2x}\frac52=(\frac25)^{x+4}$ +$(\frac25)^{2x}(\frac25)^{-1}=(\frac25)^{x+4}$ +$(\frac25)^{2x-1}=(\frac25)^{x+4}$ +$2x-1=x+4$ +$x=5$ +$K=\{5\}$ + +--- + +$36=\frac{6^{x-5}}{\sqrt6}$ +$6^2=\frac{6^{x-5}}{6^{\frac12}}$ +$6^2=6^{x-5-\frac12}$ +$2=x-5-\frac12$ +$x=\frac{15}2$ +$K=\{\frac{15}2\}$ + +--- + +$\frac{\sqrt[3]7}{49^{x-2}}=343^x*\frac17$ +$\frac{7^{\frac13}}{7^{2*(x-2)}}=7^{3x}*7^{-1}$ +$7^{\frac13-2x+4}=7^{3x-1}$ +$\frac13-2x+4=3x-1$ +$\frac13+5=5x$ +$1+15=15x$ +$16=15x$ +$x=\frac{16}{15}$ + +--- + +$2^x=32-2^x$ +$2^x=2^5-2^x$ +$2^x+2^x=2^5$ +$(2*2)^x=2^5$ +$2^x=2^4$ +$x=4$ + +--- + +$5^{x+2}2-5^{x+1}=45$ +$5^x5^22-5^{x+1}=9*5$ /$:5$ +$5^x5*2-5^x=9$ +$10*5^x-5^x=9$ +$9*5^x=9$ +$5^x=1$ +$x=0$