1003044504
Level:
A
How many solutions does the following equation have?
\[ 5^x+5^{x+1}+5^{x+2}+5^{x+3}=156 \]
Exactly one solution
No solutions
Infinitely many solutions
Exactly two solutions
A
1003044503
Level:
A
Identify the solution of the equation.
\[ 3^{x-3}-3^{x-2}=2 \]
The equation has no solution.
\( x=3 \)
\( x=-3 \)
\( x=2 \)
1003044502
Level:
A
The following exponential equation has solutions \( x_1 \) and \( x_2 \). Find the sum of \( x_1 \) and \( x_2 \).
\[ \frac{4^{x^2 }}{16^{x+1}} =16\cdot4^x \]
\( 3 \)
\( -3 \)
\( -1 \)
\( 2 \)
1003044501
Level:
A
Identify the solution of the equation.
\[ 2^{x^2-x-3}=8. \]
\( x_1=3 \), \( x_2=-2 \)
\( x_1=-3\), \( x_2=2 \)
\( x_1=0 \), \( x_2=1 \)
\( x_1=0 \), \( x_2=-1 \)
1003047003
Level:
A
We are given the equation \( \frac{8x}{x+2}+\frac{12}{x+2}=\frac{2x}{x+2} \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 8x+12=2x \)
\( \frac{4x}{x+2}+\frac6{x+2}=\frac x{x+2} \)
\( \frac{6x}{x+2}=-\frac{12}{x+2} \)
\( \frac x{x+2}=-\frac2{x+2} \)
1003047002
Level:
A
We are given the equation \( 1-\frac{5-x}2=\frac x4 \). Decide which of the following equations is equivalent to the given equation, i.e. which of the following equations was obtained from the given equation by equivalent transformations.
\( -6+2x=x \)
\( -6-2x=x \)
\( -9+2x=x \)
\( -6-x=x \)
1003047001
Level:
A
We are given the equation \( 2x^2+10x=8x+2x^2 \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 2x+10=8+2x \)
\( 10x=8x \)
\( 2x^2+2x=2x^2 \)
\( x^2+5x=4x+x^2 \)
1003044809
Level:
A
Find the domain of the equation \( \frac{2x+5}{x-2}=\frac1{x^2-1} \).
\( \mathbb{R}\setminus\{-1;1;2\} \)
\( \mathbb{R}\setminus\{1;2\} \)
\( \mathbb{R}\setminus\{-\frac52;-1;1\} \)
\( \mathbb{R}\setminus\{2\} \)
1003044808
Level:
A
Find the domain of the equation \( \frac{3x+2}{\frac x3}=1 \).
\( \mathbb{R}\setminus \{0\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus \{-\frac23\} \)
\( \mathbb{R}\setminus \{-\frac23;0\} \)
1003044807
Level:
A
Find the domain of the equation \( \frac{x+1}{x^2-3}=\frac{x^2+x-2}{2x+8} \).
\( \mathbb{R}\setminus\{-4;-\sqrt3;\sqrt3\} \)
\( \mathbb{R}\setminus\{-2;-1;1\} \)
\( \mathbb{R}\setminus\{-4;\sqrt3\} \)
\( \mathbb{R}\setminus\{-4\} \)