idk you tell me

schule/mathe/HA/MA_zu_2024-09-31.typ

@@ -0,0 +1,91 @@
+#import "@preview/grape-suite:1.0.0": exercise
+#import exercise: project, task, subtask
+
+#set text(lang: "de")
+
+#show: project.with(
+    title: "Mathe am 28.10.2024",
+    seminar: [Mathe Q2],
+    show-outline: true,
+    author: "Erik Grobecker",
+    // date: 28.10.2024,
+    show-solutions: false
+)
+
+#show math.equation: set text(font: "New Computer Modern Math")
+
+= Hausaufgaben
+
+1. Potenzregelen wiederholen & lernen
+2. S. 109 Nr. 1 d) bis j) machen 
+
+== Potenzregelen
+
+== S. 109 Nr. 1 d) bis j)
+
+*d)*\
+$
+  3 dot e^(4x) &= 16.2\
+  16.2/3 &approx 5.4\
+  ln(root(4, 5.4)) &approx 0.42\
+  ln(root(4, 16.2/3))&approx 0.42
+$
+
+basdta
+
+$
+  3 dot e^(4x) &= 16.2 &&|:3\
+  e^(4x)&=5.4 &&|ln()\
+  4x&approx 1.69 &&|:4\
+  x& approx 0.421
+$
+
+*e)*\
+$
+  e^(-x)&=10\
+  ln(e^(-x))&=ln(10)\
+  -x dot -1 &approx 2.3 dot -1\
+  x &= -2.3
+$
+
+*f)*\
+$
+  e^(4-x)&=1\
+  ln(e^(4-x))&=ln(1)\
+  4-x&=0
+  x&=4
+$
+
+*g)*\
+$
+  e^(4-4x)&=5\
+  ln(e^(4-4x))&=ln(5)\
+  (4-4x)/4 &approx 1.61/4\
+  1-x-1 &approx 0.4 -1\
+  -x dot (-1) &=-0.6 dot -1\
+  x &= 0.6
+$
+
+*h)*\
+$
+  2e^(-x)&=5\
+  (2e^(-x))/2 &=5/2\
+  -ln((2e^(-x))/2)&=-ln(5/2) approx -0.92
+$
+
+*i)*\
+$
+  e^(2x+1)&=10\
+  ln(e^(2x+1))&=ln(10)\
+  (ln(e^(2x+1))-1)/2 &=(ln(10)-1)/2 approx 0.65
+$
+
+*j)*\
+$
+  3 dot e^(0.5x-1)&=1\
+  (3 dot e^(0.5x-1))/3 &= 1/3\
+  ln((3 dot e^(0.5x-1))/3) &= ln(1/3)\
+  ln((3 dot e^(0.5x-1))/3)+1 &= ln(1/3)+1\
+  (ln((3 dot e^(0.5x-1))/3)+1) dot 2 &= (ln(1/3)+1) dot 2 approx -0.197
+$
+