2000014101
Level:
B
Find the domain of the function \(f(x)=\log_{2015}\left(\log_{\frac{1}{2015}}(\log_{2015}x)\right)\).
\((1,2015)\)
\((2015,\infty)\)
\((0,\infty)\)
\((0,2015)\)
Logarithmic Functions
2000014102
Level:
B
Make a true statement: The number \((\log_63)^2+(\log_62)^2+\log_64\cdot \log_63\) is
positive.
smaller than 1.
negative.
irrational.
2000014109
Level:
B
Identify which of the following relations is correct.
\( \log_3 10 >2\)
\( \log_2 7 >3\)
\( \log_2 3 < \log_3 2\)
\( \log_4 15 >2\)
2010011009
Level:
B
Identify which of the following relations is correct. Use the graph of \( f(x)=\log_{\frac13}x \) given below.
\( \log_{\frac13}8 < \log_{\frac13}4< \log_{\frac13} 1 < \log_{\frac13}\frac12 < \log_{\frac13}\frac15 \)
\( \log_{\frac13}\frac15 < \log_{\frac13}\frac12< \log_{\frac13} 1 < \log_{\frac13}4< \log_{\frac13}8 \)
\( \log_{\frac13}\frac12 < \log_{\frac13}\frac15< \log_{\frac13} 1 < \log_{\frac13}4 < \log_{\frac13}8 \)
\( \log_{\frac13}8 < \log_{\frac13}4< \log_{\frac13} 1 < \log_{\frac13}\frac15 < \log_{\frac13}\frac12 \)
2010016005
Level:
B
Let \(a=\log_3 \frac19\), \(b=\log_3 3\) and \(c=\log_3 \frac1{27}\). Which of the following statements is true?
\(c< a < b\)
\(c < b < a\)
\( b < c < a\)
\( a < c < b\)
2010016006
Level:
B
Let \(a=\log_4 \frac1{64}\), \(b=\log_4 4\) and \(c=\log_4 \frac1{16}\). Which of the following statements is true?
\(a< c < b\)
\(b < c < a\)
\( c < b < a\)
\( a < b < c\)
9000003803
Level:
B
The function \(g\colon y =\log _{3}(x - 2)\)
is graphed in the picture. In the following list identify a false statement.
The function \(g\)
is a positive function.
The domain of the function \(g\)
is the interval \((2,\infty )\).
The function \(g\)
is not bounded.
The function \(g\)
is an increasing function.
The function \(g\)
has neither minimum nor maximum.
The graph of the function \(g\)
goes through \([5,1]\).
9000004808
Level:
B
In the following list identify a function which is bounded below.
\(y = 3^{x}\)
\(y = -3^{x}\)
\(y =\log _{3}x\)
\(y = -\log _{3}x\)
9000004810
Level:
B
In the following list identify a function which is not an increasing function.
\(y = 4x^{2}\)
\(y =\log _{4}x\)
\(y = 4x\)
\(y = 4^{x}\)
9000004908
Level:
B
Complete the following statement: „The function
\(y =\log _{a^{2}-2a+2}x\) is
increasing if and only if ....”
\(a\in \mathbb{R}\setminus \{1\}\).
\(a\in (-\infty ,\infty )\).
\(a\in (0,\infty )\).
\(a\in (1,\infty )\).