Odpowiedź:
Zadanie 10
ODP: B
Zadanie 11
ODP: A
Zadanie 12
ODP: A
Szczegółowe wyjaśnienie:
Zadanie 10
a = [tex]\frac{-1}{27}[/tex]
b = [tex]log_{\frac{1}{4}}64[/tex]
[tex](\frac{1}{4})^{b}[/tex] = 64
[tex](\frac{1}{4})^{b}[/tex] = [tex]4^{3}[/tex]
[tex](\frac{1}{4})^{b}[/tex] = [tex](\frac{1}{4}) ^{-3}[/tex]
b = (-3)
c = [tex]log_{\frac{1}{3} } 27[/tex]
[tex](\frac{1}{3}) ^{c}[/tex] = 27
[tex](\frac{1}{3}) ^{c}[/tex] = [tex]3^{3}[/tex]
[tex](\frac{1}{3}) ^{c}[/tex] = [tex](\frac{1}{3}) ^{-3}[/tex]
c = (-3)
abc = ([tex]-\frac{1}{27}[/tex]) · -3 · -3 = ([tex]-\frac{1}{27}[/tex]) · 9 = ([tex]-\frac{9}{27}[/tex]) = [tex]-\frac{1}{3}[/tex]
Zadanie 11
[tex]2log_{5} 10[/tex] - [tex]log_{5} 4[/tex] = [tex]log_{5} 10^{2}[/tex] - [tex]log_{5} 4[/tex] = [tex]log_{5} 100[/tex] - [tex]log_{5} 4[/tex] =
= [tex]log_{5} \frac{100}{4}[/tex] = [tex]log_{5} 25[/tex] = 2
Zadanie 12
[tex]log_{3} \frac{1}{27} = x[/tex]
[tex]3^{x} = \frac{1}{27}\\\\3^{x} = 27^{-1} \\\\3^{x} = (3^{3})^{-1}\\\\3^{x} = 3^{-3}\\\\x = -3[/tex]
