2010016010
Level:
A
Given the function \(f(x)=\log_2(x+4)\), evaluate \(f(4)\cdot f(12)\).
\(12\)
\(48\)
\(128\)
\(4\)
Logarithmic functions
2010016009
Level:
A
Given the function \(f(x)=\log_2(x^2+4)\), evaluate \(f(2)\cdot f(0)\).
\(6\)
\(32\)
\(0\)
\(24\)
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?
\(a< c < b\)
\(b < c < a\)
\( c < b < a\)
\( a < b < c\)
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?
\(c< a < b\)
\(c < b < a\)
\( b < c < a\)
\( a < c < b\)
2000014109
Level:
B
Identify which of the following relations is correct.
\( \log_3 10 >2\)
\( \log_2 7 >3\)
\( \log_2 3 < \log_3 2\)
\( \log_4 15 >2\)
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.
2000014101
Level:
B
Find the domain of the function \(f(x)=\log_{2015}\left(\log_{\frac{1}{2015}}(\log_{2015}x)\right)\).
\((1;2015)\)
\((2015;\infty)\)
\((0;\infty)\)
\((0;2015)\)
2010011009
Level:
B
Identify which of the following relations is correct. Use the graph of \( f(x)=\log_{\frac13}x \) given below.
\( \log_{\frac13}8 < \log_{\frac13}4< \log_{\frac13} 1 < \log_{\frac13}\frac12 < \log_{\frac13}\frac15 \)
\( \log_{\frac13}\frac15 < \log_{\frac13}\frac12< \log_{\frac13} 1 < \log_{\frac13}4< \log_{\frac13}8 \)
\( \log_{\frac13}\frac12 < \log_{\frac13}\frac15< \log_{\frac13} 1 < \log_{\frac13}4 < \log_{\frac13}8 \)
\( \log_{\frac13}8 < \log_{\frac13}4< \log_{\frac13} 1 < \log_{\frac13}\frac15 < \log_{\frac13}\frac12 \)
2010011008
Level:
A
In the following list identify a positive expression.
\(\log _{0.5}3 -\log _{0.5}48\)
\(\log _{0.5}16 +\log _{0.5}4\)
\(\log _{3}9^3 -\log _{2}4^4\)
\(\log _{5}\left(4^{-1}\right) +\log _{5}\frac4{125}\)
2010011007
Level:
A
In the following list identify the point that is not a point on the graph of the function.
\[f(x)= -2\log _{2}x+3\]
\(\left[\frac12;1\right]\)
\([2;1]\)
\([4;-1]\)
\([1;3]\)
\(\left[\frac18;9\right]\)
\(\left[\frac14;7\right]\)