Question

Która z podanych liczb nie jest równa log1/5 4?
a) log5 1/4
b) -log25 16
c) log√5 1/√2
d) log1/√5 2
Proszę o obliczenia​

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

A.

[tex]log_5\frac{1}{4}=log_{\frac{1}{5} ^{-1}}\frac{1}{4} =-1*log_\frac{1}{5} \frac{1}{4} =log_\frac{1}{5} (\frac{1}{4} )^{-1}=log_\frac{1}{5}4[/tex]

B.

[tex]-log_{25}16=log_{5^2}16^{-1}=log_{\frac{1}{5} ^{-2}}\frac{1}{16} =-\frac{1}{2} log_\frac{1}{5} \frac{1}{16} =log_\frac{1}{5} (\frac{1}{16} )^{-\frac{1}{2} }=log_\frac{1}{5}16^\frac{1}{2} =\\=log_\frac{1}{5}4[/tex]

C.

[tex]log_{\sqrt{5}} \frac{1}{\sqrt{2} } =log_{5^\frac{1}{2} }\frac{\sqrt{2} }{2} =2log_{(\frac{1}{5} )^{-1}}\frac{\sqrt{2} }{2}=-2log_\frac{1}{5} \frac{\sqrt{2} }{2}=log_\frac{1}{5} (\frac{\sqrt{2} }{2})^{-2}=log_\frac{1}{5} (\frac{2}{\sqrt{2} } )^2=log_\frac{1}{5}\frac{4}{2} =log_\frac{1}{5}2[/tex]

 nie jest równa

D.

[tex]log_{\frac{1}{\sqrt{5} } }2=log_{\frac{1}{5} ^{\frac{1}{2}}}2=2*log_\frac{1}{5} 2=log_\frac{1}{5}2^2=log_\frac{1}{5}4[/tex]