B

2010010303

Level: 
B
We are given a sequence \( \left( \frac{2n+1}{n+3}\right)^{\infty}_{n=1}\). What are the properties of this sequence?
increasing and bounded
neither increasing nor decreasing
decreasing and bounded above
increasing and not bounded above
decreasing and not bounded above

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.
\( \log_{\frac13}8 < \log_{\frac13}⁡4< \log_{\frac13} 1 < \log_{\frac13}\frac12 < \log_{\frac13}\frac15 \)
\( \log_{\frac13}\frac15 < \log_{\frac13}⁡\frac12< \log_{\frac13} 1 < \log_{\frac13}4< \log_{\frac13}8 \)
\( \log_{\frac13}\frac12 < \log_{\frac13}⁡\frac15< \log_{\frac13} 1 < \log_{\frac13}4 < \log_{\frac13}8 \)
\( \log_{\frac13}8 < \log_{\frac13}⁡4< \log_{\frac13} 1 < \log_{\frac13}\frac15 < \log_{\frac13}\frac12 \)