1003064103
Level:
C
Find the solution set of the following inequality.
\[ \left(\frac12\right)^x\geq\left(\frac18\right) \]
\( x\in(-\infty;3] \)
\( x\in(3;\infty) \)
\( x\in(-\infty;3) \)
\( x\in[3;\infty) \)
Exponential equations and inequalities
1003064102
Level:
C
How many solutions does the following inequality have?
\[ 5^x < 0 \]
No solutions
Infinitely many solutions
Exactly one solution
Exactly two solutions
1003064101
Level:
C
Find the solution of the following inequality.
\[ 2^x\geq1 \]
\( x\in[0;\infty) \)
\( x\in(0;\infty) \)
\( x\in(-\infty;0) \)
\( x\in(-\infty;0] \)
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.
1003082606
Level:
C
How many of the following inequalities have the same solution set?
\[ \begin{aligned}
2\left(\frac14\right)^{2x-1}-\left(\frac12\right)^{4x-2}-\frac14&\leq 0 \\
2^{4x+4}-15\cdot4^{2x}&\geq 2^4 \\
9^{2x+1}-2\cdot3^5&\geq3^{4x+1}
\end{aligned} \]
\( 3 \)
\( 2 \)
\( 1 \)
\( 0 \)
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.
\( x\in(-\infty;\infty) \)
\( x\in(-\infty;-1) \)
\( x\in(-\infty;-1] \)
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.
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
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
1003082601
Level:
C
Find the set of all solutions of the following inequality.
\[ 27^x-3^{3x}\leq 3 \]
\( (-\infty;\infty) \)
\( (-\infty;0] \)
\( (-\infty;1] \)
The inequality has no solution.