Oblicz: [latex]log_{3}8 * log_{4}27- log_{8}2 =[/latex]

Oblicz: [latex]log_{3}8 * log_{4}27- log_{8}2 =[/latex]
Odpowiedź

[latex]log_{3}8 cdot log_{4}27- log_{8}2 =[/latex] [latex]frac{log8}{log3} cdot frac{log27}{log4} - frac{log2}{log8}=[/latex] [latex]frac{log2^3}{log3} cdot frac{log3^3}{log2^2} - frac{log2}{log2^3}=[/latex] [latex]frac{3log2}{log3} cdot frac{3log3}{2log2} - frac{log2}{3log2}=[/latex] [latex]frac{9}{2} - frac{1}{3}=frac{27}{6} - frac{2}{6}=frac{25}{6}=4frac{1}{6}[/latex]

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