vault backup: 2022-10-11 21:26:18

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
         }
       ]
     }

notes/mat/Funkce/Exponenciální funkce.md

@@ -160,3 +160,62 @@ $\frac{27^x3^2\sqrt3}{g^x}=1$
 ---
 
 $\sqrt[5]{(\frac43)^{1-x}}=(\frac34)^{x+3}$
+
+$(\frac43)^{\frac{1-x}5}=(\frac43)^{-x+3}$
+$\frac{1-x}5=-x-3$
+$1-x=-5x-15$
+$1=-4x-15$
+$16=-4x$
+$x=-4$
+
+$K=\{-4\}$
+
+---
+
+$0.4^{2x}*2.5=(\frac25)^{x+4}$
+
+$(\frac25)^{2x}\frac52=(\frac25)^{x+4}$
+$(\frac25)^{2x}(\frac25)^{-1}=(\frac25)^{x+4}$
+$(\frac25)^{2x-1}=(\frac25)^{x+4}$
+$2x-1=x+4$
+$x=5$
+$K=\{5\}$
+
+---
+
+$36=\frac{6^{x-5}}{\sqrt6}$
+$6^2=\frac{6^{x-5}}{6^{\frac12}}$
+$6^2=6^{x-5-\frac12}$
+$2=x-5-\frac12$
+$x=\frac{15}2$
+$K=\{\frac{15}2\}$
+
+---
+
+$\frac{\sqrt[3]7}{49^{x-2}}=343^x*\frac17$
+$\frac{7^{\frac13}}{7^{2*(x-2)}}=7^{3x}*7^{-1}$
+$7^{\frac13-2x+4}=7^{3x-1}$
+$\frac13-2x+4=3x-1$
+$\frac13+5=5x$
+$1+15=15x$
+$16=15x$
+$x=\frac{16}{15}$
+
+---
+
+$2^x=32-2^x$
+$2^x=2^5-2^x$
+$2^x+2^x=2^5$
+$(2*2)^x=2^5$
+$2^x=2^4$
+$x=4$
+
+---
+
+$5^{x+2}2-5^{x+1}=45$
+$5^x5^22-5^{x+1}=9*5$ /$:5$
+$5^x5*2-5^x=9$
+$10*5^x-5^x=9$
+$9*5^x=9$
+$5^x=1$
+$x=0$