Logarithmic functions

1003136511

Level: 
B
Identify which of the following relations is correct.
\( \log_28 > \log_2\frac72 > \log_2⁡1 > \log_2\frac47 > \log_2\frac17 \)
\( \log_2⁡\frac17 > \log_2\frac47 > \log_2 1 > \log_2\frac74 > \log_2⁡8 \)
\( \log_28 > \log_2\frac74 > \log_2\frac47 > \log_2\frac17 > \log_2⁡1 \)
\( \log_28 > \log_2\frac74 > \log_2\frac47 > \log_2⁡1 > \log_2\frac17 \)

1103136510

Level: 
B
Identify which of the following relations is correct. Use the graph of \( f(x)=\log_{0.5}x \) given below.
\( \log_{0.5}⁡\frac13 > \log_{0.5}⁡1 >\log_{0.5}⁡ \frac43 > \log_{0.5}⁡2 > \log_{0.5}⁡5 \)
\( \log_{0.5}5 > \log_{0.5}⁡2 > \log_{0.5} \frac43 > \log_{0.5}⁡1 > \log_{0.5}\frac13 \)
\( \log_{0.5}⁡1 > \log_{0.5}⁡\frac13 > \log_{0.5}⁡\frac43 > \log_{0.5}⁡2 > \log_{0.5}⁡5 \)
\( \log_{0.5}⁡\frac13 > \log_{0.5}\frac43 > \log_{0.5}1 > \log_{0.5}⁡2 > \log_{0.5}⁡5 \)

1003136502

Level: 
B
Consider the values \(\ \log_74;\) \(\log_{\frac47}{0.4};\) \(\log_40.7;\) \(\log_{\frac74}⁡4;\) \(\log_{0.7}⁡0.4;\) \(\log_{0.4}4;\) \(\log_7⁡{0.7}.\ \) Without using a calculator, determine how many of the given values are positive.
\( 4 \)
\( 3 \)
\( 2 \)
\( 5 \)