Odpowiedź:
z.1
[tex]Niech[/tex] [tex]x = log_6 2 = \frac{log_3 2}{kog_36}[/tex]
[tex]y = log_6 3 = \frac{log_3 3}{log_36}[/tex] [tex]= \frac{1}{log_36}[/tex]
więc [tex]x : y =[/tex] [tex]log_62 : log_63 = \frac{log_32}{log_36} : \frac{1}{log_36} = \frac{log_3 2}{log_36} *log_36 = log_32[/tex]
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z.2
[tex]x = log_57[/tex] [tex]y = log_75[/tex]
[tex]x*y = log_57 * log_75 = log_57*\frac{1}{log_57} = 1[/tex]
więc liczba z jest odwrotnością liczby y.
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Szczegółowe wyjaśnienie:
Wzory:
[tex]log_b c = \frac{log_ac}{log_a b}[/tex] [tex]log_a b = \frac{1}{log_b a}[/tex]
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Odpowiedź:
z.1
[tex]Niech[/tex] [tex]x = log_6 2 = \frac{log_3 2}{kog_36}[/tex]
[tex]y = log_6 3 = \frac{log_3 3}{log_36}[/tex] [tex]= \frac{1}{log_36}[/tex]
więc [tex]x : y =[/tex] [tex]log_62 : log_63 = \frac{log_32}{log_36} : \frac{1}{log_36} = \frac{log_3 2}{log_36} *log_36 = log_32[/tex]
======================================================
z.2
[tex]x = log_57[/tex] [tex]y = log_75[/tex]
[tex]x*y = log_57 * log_75 = log_57*\frac{1}{log_57} = 1[/tex]
więc liczba z jest odwrotnością liczby y.
========================================
Szczegółowe wyjaśnienie:
Wzory:
[tex]log_b c = \frac{log_ac}{log_a b}[/tex] [tex]log_a b = \frac{1}{log_b a}[/tex]
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