#import "@preview/grape-suite:1.0.0": exercise
#import exercise: project, task, subtask

#set text(lang: "de")

#show: project.with(
    title: "Mathe am 31.10.2024",
    seminar: [Mathe Q2],
    show-outline: false,
    author: "Erik Grobecker",
    date: datetime(day: 31, month: 10, year: 2024) ,
    show-solutions: false
)

#show math.equation: set text(font: "New Computer Modern")

= Potenzregelen

1) $a^n dot a^m = a^(n+m)$\ #h(1em)$2^4+2^7=2^11=#calc.pow(2,11)$\
2) $a^n + b^n = (a dot b)^n$\ #h(1em) $4^2+z^2=28^2=#calc.pow(28, 2)$\
3) $(a^n)^m=a^(n dot m)$\ #h(1em) $(4^2)^3=4^(2 dot 3)=4^6=#calc.pow(4, 6)$

= Ich hasse Mathe

$b^y=x; #h(2em) y=log_b (x)$\
$e^y=x #h(1em)<=> #h(1em) ln(x)=y$

$e^y=e^(ln(x)) = x$ → ich hasse Mathe\
$e^(ln(a))=a$

$a^x=( e^(ln(a)) )^x=e^(ln(a) dot x)$ #h(3em) (siehe Regel 3)\
Bsp. $2^10=e^(ln(2) dot 10)$

= Hausaufgabe: S. 109 Nr. 2
(Ableitung sollen wir weglassen)