1003187004
Level:
B
Let \( x\in(-\infty;0) \). The expression \( \left|x-|x|\right| +\left|x+|x|\right|+1-x|x| \) is equal to:
\( (x-1)^2 \)
\( (x+1)^2 \)
\( x^2+1 \)
\( 1-x^2 \)
B
1003187003
Level:
B
Simplifying the expression \( |3x-9|-|9-3x|+|-3x|-|-9| \) for \( x\in[3;9] \) you get:
\( 3x-9 \)
\( -3x+9 \)
\( 9x-27 \)
\( 3x+9 \)
1003187001
Level:
B
Let \( x\in(-\infty;-4] \). The value of the expression \( \left| |x|-4\right|-2|x-4|+|10-x| \) is equal to:
\( -2 \)
\( -6 \)
\( 2 \)
\( 6 \)
1003162704
Level:
B
Which of the following statements about the given equation is true?
\[ \log_4(x-1)^2=3-\frac1{\log_4(x-1)} \]
The solution set consists of two prime numbers.
The solution set is \( \left\{\frac12;1\right\} \).
The solution set is the empty set.
The equation has exactly one solution.
None of the above statements is true.
1003162703
Level:
B
How many solutions does the following equation have?
\[ \ln x^2=\ln^2 x-3 \]
exactly two positive solutions
exactly two solutions, one positive and one negative
no solutions
exactly one solution
1003162702
Level:
B
Which of the given numbers is the sum of all the solutions of the following equation?
\[ \log_2^2 x-3\log_2x+2=0 \]
\( 6 \)
\( 3 \)
\( -3 \)
\( \frac34 \)
1003162701
Level:
B
Find the solution set of the following equation.
\[ \log_3x+\frac3{\log_3x}=4 \]
\( \{3;27\} \)
\( \{1;3\} \)
\( \{-3;-1\} \)
\( \left\{\frac1{27};\frac13\right\} \)
1003159005
Level:
B
Which of the given numbers is the product of all the solutions of the following exponential equation?
\[ x^{\log_3x} =x \]
\( 3 \)
\( 0 \)
\( 1 \)
\( \frac13 \)
1003159004
Level:
B
Which of the given numbers is the sum of all the solutions of the equations \( \text{(1)} \) and \( \text{(2)} \)?
\[ \begin{aligned} 10^{x-1}&=2 &\text{(1)} \\
2^{1-x}&=5^x &\text{(2)} \end{aligned} \]
\( \log40 \)
\( \log22 \)
\( \log12+\log_72 \)
\( \log12-\log_72 \)
1003159003
Level:
B
Solve.
\[ 2^x=3^{2-x}\]
\( x=\log_69 \)
\( x=\log_96 \)
\( x=\log_59 \)
\( x=1 \)