2000000702
Level:
B
Use the given graph of the function \(f: y=-x^2-1\) to solve the inequality \(-x^2-1\leq 0\).
\(x \in \mathbb{R}\)
\(x \in \emptyset\)
\(x \in (-1;1)\)
\(x \in (-\infty;-1)\cup(1;\infty)\)
B
2000000701
Level:
B
Use the given graph of the function \(f: y=x^2-2x+1\) to solve the inequality \(x^2-2x+1>0\).
\(x \in \mathbb{R}\setminus \{1\}\)
\(x \in \mathbb{R}\setminus \{-1\}\)
\(x \in \mathbb{R}\)
\(x \in \{1\}\)
2000000506
Level:
B
Which of the equations listed below has no solution?
\(5^x +3=2\)
\(\frac{1}{2^x}-12=11\)
\(10^{x+1} +3=4.23\)
\(\left (\sqrt{3}\right)^x +2=3\)
2000000505
Level:
B
Find the number which satisfies the following equation.
\[
4^x =9
\]
\(x=2\log_{4}3\)
\(x=\frac{\log{2}}{\log 3}\)
\(x=2\log_{9}2\)
\(x=\log 9 - \log 4\)
2000000504
Level:
B
The equation \(2^x=6-3m\) with the unknown variable \(x\) and the parameter \(m\) has a solution if and only if:
\( m \in (-\infty;2)\)
\( m \in (-\infty;-2)\)
\( m \in (2;\infty)\)
\( m \in (-\infty;4)\)
2000000502
Level:
B
Find the solution of the following equation.
\[
11^{x-3}=13^{3-x}
\]
\(x=3\)
\(x=-3\)
\(x=11\)
\(x=13\)
2000000408
Level:
B
Find the solution of the following equation.
\[
4^{\log_{2}x}=1
\]
\(x=1\)
\(x=-1\)
\(x=\frac{1}{2}\)
\(x=2\)
2000000403
Level:
B
Find the solution of the following equation.
\[
\log_{3}(\log_{3}x)=0
\]
\(x=3\)
\(x=1\)
\(x=27\)
\(x=9\)
2000000205
Level:
B
Solve the following inequality.
\[
-100- x^{2} \leq 0
\]
\(x \in \mathbb{R}\)
\(x \in \mathbb{R}\setminus \{-10;10\}\)
\(x \in \emptyset \)
\(x \in (-10 ;10)\)
2000000204
Level:
B
Solve the following inequality.
\[
(5-x)^{2}\leq 0
\]
\(x \in \{5\}\)
\(x \in \mathbb{R}\setminus \{5\}\)
\(x \in \emptyset \)
\(x \in (-\infty ;-5)\cup (5;\infty )\)