miniaufgabe.js
==== 15. Januar 2024 bis 19. Januar 2024 ====
=== Montag 15. Januar 2024 ===
Lösen Sie folgende Logarithmusgleichung:miniAufgabe("#exoexpgleichungen5","#solexpgleichungen5",
[["$\\log_{2}(x) + \\log_{3}(x) = 3 + \\log_{3}(8)$", "\\[ \\begin{align*}\\log_{2}(x) + \\log_{3}(x) & = 3 + \\log_{3}(8) && | \\text{TU}\\\\\n\\log_{2}(x) + \\frac{\\log_{2}(x)}{\\log_{2}(3)} & = 3 + \\log_{3}\\left(2^{3}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 3 + 3\\log_{3}(2) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 3\\left(1 + \\log_{3}(2)\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 3\\left(1 + \\frac{\\log_{2}(2)}{\\log_{2}(3)}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) && | : \\left(1 + \\frac{1}{\\log_{2}(3)}\\right)\\\\\n\\log_{2}(x) & = 3 && |2^{(\\cdot)} \\\\\nx & = 2^{3} = 8\\\\\n\\end{align*} \\]\n"], ["$\\log_{2}(x) + \\log_{3}(x) = 4 + \\log_{3}(16)$", "\\[ \\begin{align*}\\log_{2}(x) + \\log_{3}(x) & = 4 + \\log_{3}(16) && | \\text{TU}\\\\\n\\log_{2}(x) + \\frac{\\log_{2}(x)}{\\log_{2}(3)} & = 4 + \\log_{3}\\left(2^{4}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 4 + 4\\log_{3}(2) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 4\\left(1 + \\log_{3}(2)\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 4\\left(1 + \\frac{\\log_{2}(2)}{\\log_{2}(3)}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{2}(3)}\\right) && | : \\left(1 + \\frac{1}{\\log_{2}(3)}\\right)\\\\\n\\log_{2}(x) & = 4 && |2^{(\\cdot)} \\\\\nx & = 2^{4} = 16\\\\\n\\end{align*} \\]\n"], ["$\\log_{3}(x) + \\log_{2}(x) = 3 + \\log_{2}(27)$", "\\[ \\begin{align*}\\log_{3}(x) + \\log_{2}(x) & = 3 + \\log_{2}(27) && | \\text{TU}\\\\\n\\log_{3}(x) + \\frac{\\log_{3}(x)}{\\log_{3}(2)} & = 3 + \\log_{2}\\left(3^{3}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 3 + 3\\log_{2}(3) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 3\\left(1 + \\log_{2}(3)\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 3\\left(1 + \\frac{\\log_{3}(3)}{\\log_{3}(2)}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) && | : \\left(1 + \\frac{1}{\\log_{3}(2)}\\right)\\\\\n\\log_{3}(x) & = 3 && |3^{(\\cdot)} \\\\\nx & = 3^{3} = 27\\\\\n\\end{align*} \\]\n"], ["$\\log_{3}(x) + \\log_{2}(x) = 4 + \\log_{2}(81)$", "\\[ \\begin{align*}\\log_{3}(x) + \\log_{2}(x) & = 4 + \\log_{2}(81) && | \\text{TU}\\\\\n\\log_{3}(x) + \\frac{\\log_{3}(x)}{\\log_{3}(2)} & = 4 + \\log_{2}\\left(3^{4}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 4 + 4\\log_{2}(3) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 4\\left(1 + \\log_{2}(3)\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 4\\left(1 + \\frac{\\log_{3}(3)}{\\log_{3}(2)}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{3}(2)}\\right) && | : \\left(1 + \\frac{1}{\\log_{3}(2)}\\right)\\\\\n\\log_{3}(x) & = 4 && |3^{(\\cdot)} \\\\\nx & = 3^{4} = 81\\\\\n\\end{align*} \\]\n"], ["$\\log_{2}(x) + \\log_{5}(x) = 3 + \\log_{5}(8)$", "\\[ \\begin{align*}\\log_{2}(x) + \\log_{5}(x) & = 3 + \\log_{5}(8) && | \\text{TU}\\\\\n\\log_{2}(x) + \\frac{\\log_{2}(x)}{\\log_{2}(5)} & = 3 + \\log_{5}\\left(2^{3}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 3 + 3\\log_{5}(2) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 3\\left(1 + \\log_{5}(2)\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 3\\left(1 + \\frac{\\log_{2}(2)}{\\log_{2}(5)}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) && | : \\left(1 + \\frac{1}{\\log_{2}(5)}\\right)\\\\\n\\log_{2}(x) & = 3 && |2^{(\\cdot)} \\\\\nx & = 2^{3} = 8\\\\\n\\end{align*} \\]\n"], ["$\\log_{2}(x) + \\log_{5}(x) = 4 + \\log_{5}(16)$", "\\[ \\begin{align*}\\log_{2}(x) + \\log_{5}(x) & = 4 + \\log_{5}(16) && | \\text{TU}\\\\\n\\log_{2}(x) + \\frac{\\log_{2}(x)}{\\log_{2}(5)} & = 4 + \\log_{5}\\left(2^{4}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 4 + 4\\log_{5}(2) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 4\\left(1 + \\log_{5}(2)\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 4\\left(1 + \\frac{\\log_{2}(2)}{\\log_{2}(5)}\\right) && | \\text{TU}\\\\\n\\log_{2}(x)\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{2}(5)}\\right) && | : \\left(1 + \\frac{1}{\\log_{2}(5)}\\right)\\\\\n\\log_{2}(x) & = 4 && |2^{(\\cdot)} \\\\\nx & = 2^{4} = 16\\\\\n\\end{align*} \\]\n"], ["$\\log_{5}(x) + \\log_{2}(x) = 3 + \\log_{2}(125)$", "\\[ \\begin{align*}\\log_{5}(x) + \\log_{2}(x) & = 3 + \\log_{2}(125) && | \\text{TU}\\\\\n\\log_{5}(x) + \\frac{\\log_{5}(x)}{\\log_{5}(2)} & = 3 + \\log_{2}\\left(5^{3}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 3 + 3\\log_{2}(5) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 3\\left(1 + \\log_{2}(5)\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 3\\left(1 + \\frac{\\log_{5}(5)}{\\log_{5}(2)}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) && | : \\left(1 + \\frac{1}{\\log_{5}(2)}\\right)\\\\\n\\log_{5}(x) & = 3 && |5^{(\\cdot)} \\\\\nx & = 5^{3} = 125\\\\\n\\end{align*} \\]\n"], ["$\\log_{5}(x) + \\log_{2}(x) = 4 + \\log_{2}(625)$", "\\[ \\begin{align*}\\log_{5}(x) + \\log_{2}(x) & = 4 + \\log_{2}(625) && | \\text{TU}\\\\\n\\log_{5}(x) + \\frac{\\log_{5}(x)}{\\log_{5}(2)} & = 4 + \\log_{2}\\left(5^{4}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 4 + 4\\log_{2}(5) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 4\\left(1 + \\log_{2}(5)\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 4\\left(1 + \\frac{\\log_{5}(5)}{\\log_{5}(2)}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{5}(2)}\\right) && | : \\left(1 + \\frac{1}{\\log_{5}(2)}\\right)\\\\\n\\log_{5}(x) & = 4 && |5^{(\\cdot)} \\\\\nx & = 5^{4} = 625\\\\\n\\end{align*} \\]\n"], ["$\\log_{3}(x) + \\log_{5}(x) = 3 + \\log_{5}(27)$", "\\[ \\begin{align*}\\log_{3}(x) + \\log_{5}(x) & = 3 + \\log_{5}(27) && | \\text{TU}\\\\\n\\log_{3}(x) + \\frac{\\log_{3}(x)}{\\log_{3}(5)} & = 3 + \\log_{5}\\left(3^{3}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 3 + 3\\log_{5}(3) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 3\\left(1 + \\log_{5}(3)\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 3\\left(1 + \\frac{\\log_{3}(3)}{\\log_{3}(5)}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) && | : \\left(1 + \\frac{1}{\\log_{3}(5)}\\right)\\\\\n\\log_{3}(x) & = 3 && |3^{(\\cdot)} \\\\\nx & = 3^{3} = 27\\\\\n\\end{align*} \\]\n"], ["$\\log_{3}(x) + \\log_{5}(x) = 4 + \\log_{5}(81)$", "\\[ \\begin{align*}\\log_{3}(x) + \\log_{5}(x) & = 4 + \\log_{5}(81) && | \\text{TU}\\\\\n\\log_{3}(x) + \\frac{\\log_{3}(x)}{\\log_{3}(5)} & = 4 + \\log_{5}\\left(3^{4}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 4 + 4\\log_{5}(3) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 4\\left(1 + \\log_{5}(3)\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 4\\left(1 + \\frac{\\log_{3}(3)}{\\log_{3}(5)}\\right) && | \\text{TU}\\\\\n\\log_{3}(x)\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{3}(5)}\\right) && | : \\left(1 + \\frac{1}{\\log_{3}(5)}\\right)\\\\\n\\log_{3}(x) & = 4 && |3^{(\\cdot)} \\\\\nx & = 3^{4} = 81\\\\\n\\end{align*} \\]\n"], ["$\\log_{5}(x) + \\log_{3}(x) = 3 + \\log_{3}(125)$", "\\[ \\begin{align*}\\log_{5}(x) + \\log_{3}(x) & = 3 + \\log_{3}(125) && | \\text{TU}\\\\\n\\log_{5}(x) + \\frac{\\log_{5}(x)}{\\log_{5}(3)} & = 3 + \\log_{3}\\left(5^{3}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 3 + 3\\log_{3}(5) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 3\\left(1 + \\log_{3}(5)\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 3\\left(1 + \\frac{\\log_{5}(5)}{\\log_{5}(3)}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 3\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) && | : \\left(1 + \\frac{1}{\\log_{5}(3)}\\right)\\\\\n\\log_{5}(x) & = 3 && |5^{(\\cdot)} \\\\\nx & = 5^{3} = 125\\\\\n\\end{align*} \\]\n"], ["$\\log_{5}(x) + \\log_{3}(x) = 4 + \\log_{3}(625)$", "\\[ \\begin{align*}\\log_{5}(x) + \\log_{3}(x) & = 4 + \\log_{3}(625) && | \\text{TU}\\\\\n\\log_{5}(x) + \\frac{\\log_{5}(x)}{\\log_{5}(3)} & = 4 + \\log_{3}\\left(5^{4}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 4 + 4\\log_{3}(5) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 4\\left(1 + \\log_{3}(5)\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 4\\left(1 + \\frac{\\log_{5}(5)}{\\log_{5}(3)}\\right) && | \\text{TU}\\\\\n\\log_{5}(x)\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) & = 4\\left(1 + \\frac{1}{\\log_{5}(3)}\\right) && | : \\left(1 + \\frac{1}{\\log_{5}(3)}\\right)\\\\\n\\log_{5}(x) & = 4 && |5^{(\\cdot)} \\\\\nx & = 5^{4} = 625\\\\\n\\end{align*} \\]\n"]],
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ruby exponential-gleichungen-und-logarithmen.rb 5
=== Dienstag 16. Januar 2024 ===
Lösen Sie folgende Logarithmusgleichung:miniAufgabe("#exoexpgleichungen6","#solexpgleichungen6",
[["$\\log_{7}(x) = \\frac{3}{\\log_{2}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{3}{\\log_{2}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{3}{\\frac{\\log_{7}(7)}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{3}{\\frac{1}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 3\\log_{7}(2) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(2^{3}\\right) && |7^{(\\cdot)}\\\\\nx & = 2^{3} = 8\\\\\n\\end{align*} \\]\n"], ["$\\log_{7}(x) = \\frac{4}{\\log_{2}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{4}{\\log_{2}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{4}{\\frac{\\log_{7}(7)}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{4}{\\frac{1}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 4\\log_{7}(2) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(2^{4}\\right) && |7^{(\\cdot)}\\\\\nx & = 2^{4} = 16\\\\\n\\end{align*} \\]\n"], ["$\\log_{7}(x) = \\frac{5}{\\log_{2}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{5}{\\log_{2}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{5}{\\frac{\\log_{7}(7)}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{5}{\\frac{1}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 5\\log_{7}(2) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(2^{5}\\right) && |7^{(\\cdot)}\\\\\nx & = 2^{5} = 32\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{6}{\\log_{2}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{6}{\\log_{2}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{6}{\\frac{\\log_{13}(13)}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{6}{\\frac{1}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 6\\log_{13}(2) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(2^{6}\\right) && |13^{(\\cdot)}\\\\\nx & = 2^{6} = 64\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{7}{\\log_{2}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{7}{\\log_{2}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{7}{\\frac{\\log_{13}(13)}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{7}{\\frac{1}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 7\\log_{13}(2) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(2^{7}\\right) && |13^{(\\cdot)}\\\\\nx & = 2^{7} = 128\\\\\n\\end{align*} \\]\n"], ["$\\log_{7}(x) = \\frac{8}{\\log_{2}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{8}{\\log_{2}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{8}{\\frac{\\log_{7}(7)}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{8}{\\frac{1}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 8\\log_{7}(2) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(2^{8}\\right) && |7^{(\\cdot)}\\\\\nx & = 2^{8} = 256\\\\\n\\end{align*} \\]\n"], ["$\\log_{7}(x) = \\frac{9}{\\log_{2}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{9}{\\log_{2}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{9}{\\frac{\\log_{7}(7)}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{9}{\\frac{1}{\\log_{7}(2)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 9\\log_{7}(2) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(2^{9}\\right) && |7^{(\\cdot)}\\\\\nx & = 2^{9} = 512\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{10}{\\log_{2}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{10}{\\log_{2}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{10}{\\frac{\\log_{13}(13)}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{10}{\\frac{1}{\\log_{13}(2)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 10\\log_{13}(2) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(2^{10}\\right) && |13^{(\\cdot)}\\\\\nx & = 2^{10} = 1024\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{3}{\\log_{3}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{3}{\\log_{3}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{3}{\\frac{\\log_{13}(13)}{\\log_{13}(3)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{3}{\\frac{1}{\\log_{13}(3)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 3\\log_{13}(3) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(3^{3}\\right) && |13^{(\\cdot)}\\\\\nx & = 3^{3} = 27\\\\\n\\end{align*} \\]\n"], ["$\\log_{11}(x) = \\frac{4}{\\log_{3}(11)}$", "\\[ \\begin{align*} \\log_{11}(x) & = \\frac{4}{\\log_{3}(11)} && |\\text{LS Basiswechsel zu Basis 11}\\\\\n\\log_{11}(x) & = \\frac{4}{\\frac{\\log_{11}(11)}{\\log_{11}(3)}} && |\\text{TU}\\\\\n\\log_{11}(x) & = \\frac{4}{\\frac{1}{\\log_{11}(3)}} && |\\text{TU}\\\\\n\\log_{11}(x) & = 4\\log_{11}(3) && |\\text{TU}\\\\\n\\log_{11}(x) & = \\log_{11}\\left(3^{4}\\right) && |11^{(\\cdot)}\\\\\nx & = 3^{4} = 81\\\\\n\\end{align*} \\]\n"], ["$\\log_{11}(x) = \\frac{3}{\\log_{4}(11)}$", "\\[ \\begin{align*} \\log_{11}(x) & = \\frac{3}{\\log_{4}(11)} && |\\text{LS Basiswechsel zu Basis 11}\\\\\n\\log_{11}(x) & = \\frac{3}{\\frac{\\log_{11}(11)}{\\log_{11}(4)}} && |\\text{TU}\\\\\n\\log_{11}(x) & = \\frac{3}{\\frac{1}{\\log_{11}(4)}} && |\\text{TU}\\\\\n\\log_{11}(x) & = 3\\log_{11}(4) && |\\text{TU}\\\\\n\\log_{11}(x) & = \\log_{11}\\left(4^{3}\\right) && |11^{(\\cdot)}\\\\\nx & = 4^{3} = 64\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{4}{\\log_{4}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{4}{\\log_{4}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{4}{\\frac{\\log_{13}(13)}{\\log_{13}(4)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{4}{\\frac{1}{\\log_{13}(4)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 4\\log_{13}(4) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(4^{4}\\right) && |13^{(\\cdot)}\\\\\nx & = 4^{4} = 256\\\\\n\\end{align*} \\]\n"], ["$\\log_{7}(x) = \\frac{5}{\\log_{4}(7)}$", "\\[ \\begin{align*} \\log_{7}(x) & = \\frac{5}{\\log_{4}(7)} && |\\text{LS Basiswechsel zu Basis 7}\\\\\n\\log_{7}(x) & = \\frac{5}{\\frac{\\log_{7}(7)}{\\log_{7}(4)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = \\frac{5}{\\frac{1}{\\log_{7}(4)}} && |\\text{TU}\\\\\n\\log_{7}(x) & = 5\\log_{7}(4) && |\\text{TU}\\\\\n\\log_{7}(x) & = \\log_{7}\\left(4^{5}\\right) && |7^{(\\cdot)}\\\\\nx & = 4^{5} = 1024\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{3}{\\log_{5}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{3}{\\log_{5}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{3}{\\frac{\\log_{13}(13)}{\\log_{13}(5)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{3}{\\frac{1}{\\log_{13}(5)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 3\\log_{13}(5) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(5^{3}\\right) && |13^{(\\cdot)}\\\\\nx & = 5^{3} = 125\\\\\n\\end{align*} \\]\n"], ["$\\log_{13}(x) = \\frac{4}{\\log_{5}(13)}$", "\\[ \\begin{align*} \\log_{13}(x) & = \\frac{4}{\\log_{5}(13)} && |\\text{LS Basiswechsel zu Basis 13}\\\\\n\\log_{13}(x) & = \\frac{4}{\\frac{\\log_{13}(13)}{\\log_{13}(5)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = \\frac{4}{\\frac{1}{\\log_{13}(5)}} && |\\text{TU}\\\\\n\\log_{13}(x) & = 4\\log_{13}(5) && |\\text{TU}\\\\\n\\log_{13}(x) & = \\log_{13}\\left(5^{4}\\right) && |13^{(\\cdot)}\\\\\nx & = 5^{4} = 625\\\\\n\\end{align*} \\]\n"]],
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ruby exponential-gleichungen-und-logarithmen.rb 6