1003082602
Level:
C
How many solutions does the following inequality in the set of positive integers have?
\[ 9^{x+2}-5\cdot9^{x+1} \leq 2916 \]
\( 2 \)
\( 3 \)
\( 1 \)
Infinitely many solutions
Exponential equations and inequalities
1003082603
Level:
C
How many solutions does the following inequality have?
\[ 2^{x-1}-2^{x-3}-2^{x-4} \geq 2^{-4}-2^{-3}-2^{-2} \]
Infinitely many solutions
No solution
Exactly one solution
Exactly two solutions
1003082604
Level:
C
Find the solution set of the following inequality.
\[ \mathrm{e}^{x+2}+\mathrm{e}\leq\mathrm{e}^{x+1}+\mathrm{e}^2 \]
\( (-\infty;0] \)
\( (-\infty;-1] \)
\( (-\infty;\infty) \)
The inequality has no solution.
1003082605
Level:
C
Solve the following system of two inequalities.
\begin{align*} \left(\frac12\right)^{x+1}-3\left(\frac12\right)^{x+2}+\frac12&\geq0\\ 4^{x+2}-3\cdot4^{x+1} &< 1 \end{align*}
The system of inequalities has no solution.
\( x\in(-\infty;\infty) \)
\( x\in(-\infty;-1) \)
\( x\in(-\infty;-1] \)
1003082606
Level:
C
How many of the following inequalities have the same solution set?
\[ \begin{aligned}
2\left(\frac14\right)^{2x-1}-\left(\frac12\right)^{4x-2}-\frac14&\leq 0 \\
2^{4x+4}-15\cdot4^{2x}&\geq 2^4 \\
9^{2x+1}-2\cdot3^5&\geq3^{4x+1}
\end{aligned} \]
\( 3 \)
\( 2 \)
\( 1 \)
\( 0 \)
1003082607
Level:
C
Find the set of all solutions of the following inequality.
\[ 4^{x+3}-2\cdot5^{x+2} < 5^{x+2}+4^{x+1} \]
\( (-1;\infty) \)
\( (-\infty;-1) \)
\( (1;\infty) \)
The inequality has no solution.
1103064105
Level:
C
Decide which of the following diagrams shows the solution set of the given inequality.
\[ 16\cdot4^{2x-3} < 64^{x+1} \]
1103064107
Level:
C
Decide which of the following diagrams shows the solution set of the given inequality.
\[ \left(\frac13\right)^{x(x+1)} \geq\left(\frac1{27}\right)^2 \]
2000000301
Level:
C
Find the value of the parameter \( m \) so that the solution set of the inequality
\[
\left(\frac{1}{7}\right)^x \leq m
\]
is the interval \([ 2;\infty)\).
\( m = \frac{1}{49} \)
\( m = 49\)
\(m = 2\)
\( m=14\)
2000000501
Level:
C
The set of all solutions of the inequality \(0.7^{-x} > 0.7^{4+x}\) is the interval:
\( (-2 ;\infty)\)
\( (-\infty;2)\)
\( (2 ;\infty)\)
\( (-\infty ;-2)\)