2010008204
Level:
A
Identify the solution of the equation.
\[ 4^x+2\cdot 16^{x}-1=0\]
\(x=-\frac{1}{2}\)
\(x=\frac12\)
\(x=0\)
\(x=4\)
Exponential equations and inequalities
2010008203
Level:
A
Identify the solution of the equation.
\[ 3^x+3^{x+1}+3^{x+3}=93 \]
\(x=1\)
\(x=2\)
\(x=0\)
\(x=4\)
2010008202
Level:
A
Identify the solution of the equation.
\[ 2^x+2^{x+2}+2^{x+4}=84 \]
\(x=2\)
\(x=1\)
\(x=0\)
\(x=4\)
2010008201
Level:
B
How many solutions does the following equation have?
\[ 49^x+4\cdot7^x=5 \]
Exactly one solution
Exactly two solutions
No solutions
Infinitely many solutions
2000003001
Level:
B
Which of the given numbers is the solution of the equation
\( 3^{2x} + \frac{4}{27} = 2\cdot 3^{2x+1}-9^x\)?
\( x=-\frac{3}{2} \)
\( x=1 \)
\( x=\frac{3}{2} \)
\( x=-1\)
2000000507
Level:
C
Find the solution set of the following inequality.
\[
16^x -4^x\leq 0
\]
\( (-\infty; 0] \)
\( [ 0; \infty) \)
\( [ 1; \infty) \)
\( (-\infty; 1] \)
2000000506
Level:
B
Which of the equations listed below has no solution?
\(5^x +3=2\)
\(\frac{1}{2^x}-12=11\)
\(10^{x+1} +3=4.23\)
\(\left (\sqrt{3}\right)^x +2=3\)
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:
\( m \in (-\infty;2)\)
\( m \in (-\infty;-2)\)
\( m \in (2;\infty)\)
\( m \in (-\infty;4)\)
2000000503
Level:
C
The set of all solutions of the inequality \(4^{\frac{2}{x+3}}>1\) is the interval:
\( (-3;\infty)\)
\( (-\infty;3)\)
\( (3;\infty)\)
\( (-\infty;-3)\)
2000000502
Level:
B
Find the solution of the following equation.
\[
11^{x-3}=13^{3-x}
\]
\(x=3\)
\(x=-3\)
\(x=11\)
\(x=13\)