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proszę o pomoc w zadaniu
[tex]a) log_{2}0.5[/tex]
[tex]b) log_{3}1[/tex]
[tex]c)log100[/tex]
[tex]d) log0.1[/tex]
[tex]e) log \sqrt{1000} [/tex]
[tex]f) log_{5} \sqrt{5} [/tex]
[tex] log_{5}0.04[/tex]


Odpowiedź :

[tex]a) \ log_{2}0,5 = lo_{2}\frac{1}{2} = log_{2}2^{-1} = -1\\\\b) \ log_{3}1 = log_{3}3^{0} = 0\\\\c) \ log100 = log10^{2} = 2\\\\d) \ log0,1 = log\frac{1}{10} = log10^{-1} = -1\\\\e) \ log\sqrt{1000}=log1000^{\frac{1}{2}} = log(10^{3})^{\frac{1}{2}} =log10^{\frac{3}{2}} = \frac{3}{2}\\\\f) \ log_{5}\sqrt{5} = log_{5}5^{\frac{1}{2}} = \frac{1}{2}\\\\h) \ log_{5}0,04 =log_{5}\frac{4}{100} = log_{5}\frac{1}{25}=log_{5}(\frac{1}{5})^{2} = log_{5}5^{-2} = -2[/tex]