1103138401
Level:
C
From the following functions choose the one which is graphed in the picture.
\( f(x)=\left|\log_{\frac12}x\right| \)
\( g(x) = \log_{\frac12}|x| \)
\( k(x)=\log_{\frac12}\sqrt x \)
\( m(x)=\sqrt{\log_{\frac12}x} \)
Logarithmic functions
1003136511
Level:
B
Identify which of the following relations is correct.
\( \log_28 > \log_2\frac72 > \log_21 > \log_2\frac47 > \log_2\frac17 \)
\( \log_2\frac17 > \log_2\frac47 > \log_2 1 > \log_2\frac74 > \log_28 \)
\( \log_28 > \log_2\frac74 > \log_2\frac47 > \log_2\frac17 > \log_21 \)
\( \log_28 > \log_2\frac74 > \log_2\frac47 > \log_21 > \log_2\frac17 \)
1103136510
Level:
B
Identify which of the following relations is correct. Use the graph of \( f(x)=\log_{0.5}x \) given below.
\( \log_{0.5}\frac13 > \log_{0.5}1 >\log_{0.5} \frac43 > \log_{0.5}2 > \log_{0.5}5 \)
\( \log_{0.5}5 > \log_{0.5}2 > \log_{0.5} \frac43 > \log_{0.5}1 > \log_{0.5}\frac13 \)
\( \log_{0.5}1 > \log_{0.5}\frac13 > \log_{0.5}\frac43 > \log_{0.5}2 > \log_{0.5}5 \)
\( \log_{0.5}\frac13 > \log_{0.5}\frac43 > \log_{0.5}1 > \log_{0.5}2 > \log_{0.5}5 \)
1003136509
Level:
B
How many of the following inequalities is/are true?
\begin{align*}
\log_74 & > \log_711; & \log_{0.4} 0.7 &\leq \log_{0.4}3 \\ \log_{\frac17}4 &\geq \log_{\frac17}0.4; & \log_30.11 & < \log_36 \end{align*}
\( 1 \)
\( 2 \)
\( 3 \)
\( 0 \)
1003136508
Level:
B
What are the values of the real parameter \( a \), that satisfy inequality \( \log_a7 < \log_a4 \)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)
1003136507
Level:
B
What are the values of the real parameter \( a \), that satisfy inequality \( \log_a\frac47 > \log_a \frac74 \)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)
1103136506
Level:
B
What are the values of the real variable \( x \), if \( \log_4x \leq \log_40.7 \)? Use the graph of \( f(x)=\log_4x \) given below.
\( x\in(0;0.7] \)
\( x\in[0.7;\infty) \)
\( x\in[1;\infty) \)
\( x\in(-\infty;0.7] \)
1103136505
Level:
B
What are the values of the real variable \( x \), if \( \log_{\frac14}x > \log_{\frac14}3 \)? Use the graph of \( f(x)=\log_{\frac14}x \) given below.
\( x\in(0;3) \)
\( x\in(-\infty;3) \)
\( x\in(3;\infty) \)
\( x\in(0;\infty) \)
1103136504
Level:
B
What are the values of the real variable \( x \), if \( \log_7x < 0 \)? Use the graph of \( f(x)=\log_7x \) given below.
\( x\in(0;1) \)
\( x\in[1;\infty) \)
\( x\in(0;\infty) \)
\( x\in[0;1] \)
1103136503
Level:
B
What are the values of the real variable \( x \), if \( \log_{0.4}x \leq 0 \)? Use the graph of \( f(x)=\log_{0.4}x \) given below.
\( x\in[1;\infty) \)
\( x\in(0;1] \)
\( x\in(-\infty;0] \)
\( x\in[0;\infty) \)