2000014101 Level: BFind the domain of the function \(f(x)=\log_{2015}\left(\log_{\frac{1}{2015}}(\log_{2015}x)\right)\).\((1;2015)\)\((2015;\infty)\)\((0;\infty)\)\((0;2015)\)
2000014102 Level: BMake a true statement: The number \((\log_63)^2+(\log_62)^2+\log_64\cdot \log_63\) ispositive.smaller than 1.negative.irrational.
2000014109 Level: BIdentify 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: BIdentify 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: BLet \(a=\log_3 \frac19\); \(b=\log_3 3\) 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: BLet \(a=\log_4 \frac1{64}\); \(b=\log_4 4\) 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: BThe 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: BIn 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: BIn 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: BComplete the following statement: „The function \(y =\log _{a^{2}-2a+2}x\) is increasing if and only if ....”\(a\in \mathbb{R}\setminus \{1\}\).\(a\in (-\infty ;\infty )\).\(a\in (0;\infty )\).\(a\in (1;\infty )\).