lehrkraefte:blc:miniaufgaben:kw17-2025 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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==== 28. April 2025 bis 2. Mai 2025 ====
=== Montag 28. April 2025 ===
Keine Miniaufgabe
=== Donnerstag 1. Mai 2025 ===

Wenden Sie Logarithmengesetze an und schreiben Sie als Summe von Vielfachen von $\log_a(x)$ und $\log_a(y)$.<JS>miniAufgabe("#exoexpgleichungen3","#solexpgleichungen3",
[["$\\log_a\\left(\\left(x^{5} y^{-4}\\right)^{3}\\right) + \\log_a\\left(\\left(x^{5} y^{-3}\\right)^{-5}\\right)$", "$\\log_a\\left(\\left(x^{5} y^{-4}\\right)^{3}\\right) + \\log_a\\left(\\left(x^{5} y^{-3}\\right)^{-5}\\right) = \\log_a\\left(x^{15} y^{-12}\\right) + \\log_a\\left(x^{-25} y^{15}\\right) = \\log_a\\left(x^{15}\\right) + \\log_a\\left(y^{-12}\\right) + \\log_a\\left(x^{-25}\\right) + \\log_a\\left(y^{15}\\right) =$\n<br>$15\\log_a\\left(x\\right) -12 \\log_a\\left(y\\right)-25\\log_a\\left(x\\right) +15 \\log_a\\left(y\\right) = -10 \\log_a(x) +3\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{-5} y^{3}\\right)^{5}\\right) + \\log_a\\left(\\left(x^{2} y^{-3}\\right)^{-3}\\right)$", "$\\log_a\\left(\\left(x^{-5} y^{3}\\right)^{5}\\right) + \\log_a\\left(\\left(x^{2} y^{-3}\\right)^{-3}\\right) = \\log_a\\left(x^{-25} y^{15}\\right) + \\log_a\\left(x^{-6} y^{9}\\right) = \\log_a\\left(x^{-25}\\right) + \\log_a\\left(y^{15}\\right) + \\log_a\\left(x^{-6}\\right) + \\log_a\\left(y^{9}\\right) =$\n<br>$-25\\log_a\\left(x\\right) +15 \\log_a\\left(y\\right)-6\\log_a\\left(x\\right) +9 \\log_a\\left(y\\right) = -31 \\log_a(x) +24\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{6} y^{-4}\\right)^{5}\\right) + \\log_a\\left(\\left(x^{-5} y^{3}\\right)^{-3}\\right)$", "$\\log_a\\left(\\left(x^{6} y^{-4}\\right)^{5}\\right) + \\log_a\\left(\\left(x^{-5} y^{3}\\right)^{-3}\\right) = \\log_a\\left(x^{30} y^{-20}\\right) + \\log_a\\left(x^{15} y^{-9}\\right) = \\log_a\\left(x^{30}\\right) + \\log_a\\left(y^{-20}\\right) + \\log_a\\left(x^{15}\\right) + \\log_a\\left(y^{-9}\\right) =$\n<br>$30\\log_a\\left(x\\right) -20 \\log_a\\left(y\\right)+15\\log_a\\left(x\\right) -9 \\log_a\\left(y\\right) = 45 \\log_a(x) -29\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{-6} y^{5}\\right)^{6}\\right) + \\log_a\\left(\\left(x^{4} y^{-2}\\right)^{-5}\\right)$", "$\\log_a\\left(\\left(x^{-6} y^{5}\\right)^{6}\\right) + \\log_a\\left(\\left(x^{4} y^{-2}\\right)^{-5}\\right) = \\log_a\\left(x^{-36} y^{30}\\right) + \\log_a\\left(x^{-20} y^{10}\\right) = \\log_a\\left(x^{-36}\\right) + \\log_a\\left(y^{30}\\right) + \\log_a\\left(x^{-20}\\right) + \\log_a\\left(y^{10}\\right) =$\n<br>$-36\\log_a\\left(x\\right) +30 \\log_a\\left(y\\right)-20\\log_a\\left(x\\right) +10 \\log_a\\left(y\\right) = -56 \\log_a(x) +40\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{-6} y^{5}\\right)^{3}\\right) + \\log_a\\left(\\left(x^{4} y^{-5}\\right)^{-4}\\right)$", "$\\log_a\\left(\\left(x^{-6} y^{5}\\right)^{3}\\right) + \\log_a\\left(\\left(x^{4} y^{-5}\\right)^{-4}\\right) = \\log_a\\left(x^{-18} y^{15}\\right) + \\log_a\\left(x^{-16} y^{20}\\right) = \\log_a\\left(x^{-18}\\right) + \\log_a\\left(y^{15}\\right) + \\log_a\\left(x^{-16}\\right) + \\log_a\\left(y^{20}\\right) =$\n<br>$-18\\log_a\\left(x\\right) +15 \\log_a\\left(y\\right)-16\\log_a\\left(x\\right) +20 \\log_a\\left(y\\right) = -34 \\log_a(x) +35\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{2} y^{-6}\\right)^{-6}\\right) + \\log_a\\left(\\left(x^{3} y^{-2}\\right)^{2}\\right)$", "$\\log_a\\left(\\left(x^{2} y^{-6}\\right)^{-6}\\right) + \\log_a\\left(\\left(x^{3} y^{-2}\\right)^{2}\\right) = \\log_a\\left(x^{-12} y^{36}\\right) + \\log_a\\left(x^{6} y^{-4}\\right) = \\log_a\\left(x^{-12}\\right) + \\log_a\\left(y^{36}\\right) + \\log_a\\left(x^{6}\\right) + \\log_a\\left(y^{-4}\\right) =$\n<br>$-12\\log_a\\left(x\\right) +36 \\log_a\\left(y\\right)+6\\log_a\\left(x\\right) -4 \\log_a\\left(y\\right) = -6 \\log_a(x) +32\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{-2} y^{6}\\right)^{-2}\\right) + \\log_a\\left(\\left(x^{4} y^{-6}\\right)^{4}\\right)$", "$\\log_a\\left(\\left(x^{-2} y^{6}\\right)^{-2}\\right) + \\log_a\\left(\\left(x^{4} y^{-6}\\right)^{4}\\right) = \\log_a\\left(x^{4} y^{-12}\\right) + \\log_a\\left(x^{16} y^{-24}\\right) = \\log_a\\left(x^{4}\\right) + \\log_a\\left(y^{-12}\\right) + \\log_a\\left(x^{16}\\right) + \\log_a\\left(y^{-24}\\right) =$\n<br>$4\\log_a\\left(x\\right) -12 \\log_a\\left(y\\right)+16\\log_a\\left(x\\right) -24 \\log_a\\left(y\\right) = 20 \\log_a(x) -36\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{-3} y^{6}\\right)^{2}\\right) + \\log_a\\left(\\left(x^{2} y^{-6}\\right)^{-4}\\right)$", "$\\log_a\\left(\\left(x^{-3} y^{6}\\right)^{2}\\right) + \\log_a\\left(\\left(x^{2} y^{-6}\\right)^{-4}\\right) = \\log_a\\left(x^{-6} y^{12}\\right) + \\log_a\\left(x^{-8} y^{24}\\right) = \\log_a\\left(x^{-6}\\right) + \\log_a\\left(y^{12}\\right) + \\log_a\\left(x^{-8}\\right) + \\log_a\\left(y^{24}\\right) =$\n<br>$-6\\log_a\\left(x\\right) +12 \\log_a\\left(y\\right)-8\\log_a\\left(x\\right) +24 \\log_a\\left(y\\right) = -14 \\log_a(x) +36\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{4} y^{-3}\\right)^{-3}\\right) + \\log_a\\left(\\left(x^{3} y^{-4}\\right)^{5}\\right)$", "$\\log_a\\left(\\left(x^{4} y^{-3}\\right)^{-3}\\right) + \\log_a\\left(\\left(x^{3} y^{-4}\\right)^{5}\\right) = \\log_a\\left(x^{-12} y^{9}\\right) + \\log_a\\left(x^{15} y^{-20}\\right) = \\log_a\\left(x^{-12}\\right) + \\log_a\\left(y^{9}\\right) + \\log_a\\left(x^{15}\\right) + \\log_a\\left(y^{-20}\\right) =$\n<br>$-12\\log_a\\left(x\\right) +9 \\log_a\\left(y\\right)+15\\log_a\\left(x\\right) -20 \\log_a\\left(y\\right) = 3 \\log_a(x) -11\\log_a(y)$"], ["$\\log_a\\left(\\left(x^{6} y^{-3}\\right)^{2}\\right) + \\log_a\\left(\\left(x^{5} y^{-2}\\right)^{-4}\\right)$", "$\\log_a\\left(\\left(x^{6} y^{-3}\\right)^{2}\\right) + \\log_a\\left(\\left(x^{5} y^{-2}\\right)^{-4}\\right) = \\log_a\\left(x^{12} y^{-6}\\right) + \\log_a\\left(x^{-20} y^{8}\\right) = \\log_a\\left(x^{12}\\right) + \\log_a\\left(y^{-6}\\right) + \\log_a\\left(x^{-20}\\right) + \\log_a\\left(y^{8}\\right) =$\n<br>$12\\log_a\\left(x\\right) -6 \\log_a\\left(y\\right)-20\\log_a\\left(x\\right) +8 \\log_a\\left(y\\right) = -8 \\log_a(x) +2\\log_a(y)$"]],
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<div style='font-size:12px;color:gray;'>ruby exponential-gleichungen-und-logarithmen.rb 3</div>
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