1003030101
Level:
A
Solve.
\[ 2^x=-4\]
The equation has no solution.
\( x=2 \)
\( x=-2 \)
\( x=-\frac12 \)
Exponential equations and inequalities
1003030102
Level:
A
Solve.
\[ 5^{8-2x}=1\]
\( x=4 \)
\( x=-4 \)
\( x=\frac72 \)
The equation has no solution.
1003030103
Level:
A
Solve.
\[ 8^{2x}=16\sqrt[3]4\]
\( x=\frac79 \)
\( x=\frac{11}{12} \)
\( x=\frac49 \)
\( x=\frac13 \)
1003030104
Level:
A
Decide which of the following intervals contains \( d \), if \( \left(0.1^{d-1}\right)^3=10^{d-1} \).
\( [-1;3] \)
\( [9;13] \)
\( [4;8] \)
\( [-6;-2] \)
1003030105
Level:
A
How many solutions does the following equation have?
\[ \sqrt{81^{x+1}}=3^{2x}\]
No solutions
Infinitely many solutions
Exactly one solution
Exactly two solutions
1003030106
Level:
A
How many solutions does the following equation have?
\[ 2^x\cdot5^x=100^{3-x} \]
Exactly one solution
No solutions
Infinitely many solutions
Exactly two solutions
1003030107
Level:
A
Solve.
\[ \sqrt[2x+6]{9^{x+2}}=\sqrt[6]{243}\]
\( x=3 \)
\( x=-8 \)
\( x=\frac{-24}7 \)
\( x=-3 \)
1003044501
Level:
A
Identify the solution of the equation.
\[ 2^{x^2-x-3}=8. \]
\( x_1=3 \), \( x_2=-2 \)
\( x_1=-3\), \( x_2=2 \)
\( x_1=0 \), \( x_2=1 \)
\( x_1=0 \), \( x_2=-1 \)
1003044502
Level:
A
The following exponential equation has solutions \( x_1 \) and \( x_2 \). Find the sum of \( x_1 \) and \( x_2 \).
\[ \frac{4^{x^2 }}{16^{x+1}} =16\cdot4^x \]
\( 3 \)
\( -3 \)
\( -1 \)
\( 2 \)
1003044503
Level:
A
Identify the solution of the equation.
\[ 3^{x-3}-3^{x-2}=2 \]
The equation has no solution.
\( x=3 \)
\( x=-3 \)
\( x=2 \)