Matematik
logaritme
UDEN HJÆLPEMIDLER!!
Funktionen <span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">f(x)=b·x^a <span style="mso-fareast-font-family: "Times New Roman";mso-fareast-theme-font:minor-fareast">opfylder, at f(2)=2 og f(4)=16</o:p>
<span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">Bestem tallene a og b:</o:p>
<span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">Vi benytter formlen forneden:</o:p>
<span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">a=(log(y_2)-log(y_1))/(log(x_2)-log(x_1))
<span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">a=(log(16)-log(2))/(log(4)-log(2))
<span style="mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast">Er der nogen, der kan hjælpe mig? Jeg kan ikke komme videre.
Svar #1
11. maj 2011 af mathon
(16/2) = (4/2)a
8 = 2a
23 = 2a
a = 3
dvs
f(x) = y = b·x3
2 = b·23
b = 2/8 = (1/4)
konklusion:
f(x) = (1/4)·x3
Svar #3
11. maj 2011 af NejTilSvampe
eller
8 = 2^a
log(8) = log(2^3) = a*log(2)
a = 3* log(2) / log(2) = 3
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