B

2010010106

Level: 
B
Which of the following statements about the given equation is true? \[ \log_2(x-2)^2=4-\frac2{\log_2⁡(x-2)} \]
The equation has exactly one solution.
The solution set consists of two prime numbers.
The solution set is the empty set.
None of the above statements is true.

2010011009

Level: 
B
Identify which of the following relations is correct. Use the graph of \( f(x)=\log_{\frac13}x \) given below.
\( \log_{\frac13}8 < \log_{\frac13}⁡4< \log_{\frac13} 1 < \log_{\frac13}\frac12 < \log_{\frac13}\frac15 \)
\( \log_{\frac13}\frac15 < \log_{\frac13}⁡\frac12< \log_{\frac13} 1 < \log_{\frac13}4< \log_{\frac13}8 \)
\( \log_{\frac13}\frac12 < \log_{\frac13}⁡\frac15< \log_{\frac13} 1 < \log_{\frac13}4 < \log_{\frac13}8 \)
\( \log_{\frac13}8 < \log_{\frac13}⁡4< \log_{\frac13} 1 < \log_{\frac13}\frac15 < \log_{\frac13}\frac12 \)

2010011005

Level: 
B
If \( a \), \( b \), \( c\in(0;\infty) \) then the expression \( \log_2a+3 \log_2 b-\frac12 \log_2⁡c \) is equivalent to:
\( \log_2\frac{ab^3}{\sqrt{c}} \)
\( \log_2\frac{3ab}{\frac12 c} \)
\( \log_2 \left({ab^3}{c}^{\frac12} \right)\)
\( \log_2 \left(-\frac32 abc\right) \)