Oblicz logarytmy

[SPORE6]

Oblicz:
a) \(\frac{\log_6125}{\log_65}\)
b) \(\frac{\log_45}{\log_25}\)
c) \(\log_2(\log_3 \sqrt{5}) - \log_2(\log_35)\)

[radagast]

Oblicz:
a) \(\frac{\log_6125}{\log_65}\)
b) \(\frac{\log_45}{\log_25}\)
c) \(\log_2(\log_3 \sqrt{5}) - \log_2(\log_35)\)

a) \(\frac{\log_6125}{\log_65}=\log_5 125=3\)
b) \(\frac{\log_45}{\log_25}=\frac{\log_52}{\log_54}=\log_42= \frac{1}{2}\)
c) \(\log_2(\log_3 \sqrt{5}) - \log_2(\log_35)=\log_2 \frac{\log_3 \sqrt{5}}{\log_35}=\log_2 \log_5 \sqrt{5}=\log_2 \frac{1}{2} =-1\)

[Galen]

c) Różnica logarytmów= log ilorazu
\(log_2( \frac{log_35^{ \frac{1}{2} }}{log_35} )=log_2( \frac{ \frac{1}{2}log_35 }{log_35} )=log_2( \frac{1}{2})=-1\)