Logarithmic functions

1003136511

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

1103118504

Level: 
B
Given the next graph of a logarithmic function \( f \), choose the correct list of properties of \( f \).
decreasing, asymptote at \( x=0 \), unbounded
decreasing, asymptote at \( y=0 \), unbounded
decreasing, asymptote at \( x=0 \), bounded below
increasing, asymptote at \( y=0 \), bounded below

1103136501

Level: 
B
Consider the values \( \log_{0.2}⁡3;\) \(\log_20.3;\) \(\log_{0.3}⁡1;\) \(\log_2⁡3;\) \(\log_{\frac32}⁡\frac23;\) \(\log_{\frac23}⁡2;\) \(\log_{0.3}\frac32.\) Determine how many of the given values are negative. Use the graph of a logarithmic function given below.
\( 5 \)
\( 4 \)
\( 3 \)
\( 2 \)

1103136510

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