1003044601
Level:
B
Identify the solution of the equation.
\[ 4^{2x}-20\cdot4^x=-64\]
\( x_1=1;\ x_2=2 \)
\( x_1=16;\ x_2=4 \)
\( x_1=-16;\ x_2=-4 \)
\( x_1=1;\ x_2=4 \)
Exponential Equations and Inequalities
1003030107
Level:
A
Solve.
\[ \sqrt[2x+6]{9^{x+2}}=\sqrt[6]{243}\]
\( x=3 \)
\( x=-8 \)
\( x=\frac{-24}7 \)
\( x=-3 \)
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
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
1003030104
Level:
A
Decide which of the following intervals contains \( d \), if \( \left(0.1^{d-1}\right)^3=10^{d-1} \).
\( [-1;3] \)
\( [9;13] \)
\( [4;8] \)
\( [-6;-2] \)
1003030103
Level:
A
Solve.
\[ 8^{2x}=16\sqrt[3]4\]
\( x=\frac79 \)
\( x=\frac{11}{12} \)
\( x=\frac49 \)
\( x=\frac13 \)
1003030102
Level:
A
Solve.
\[ 5^{8-2x}=1\]
\( x=4 \)
\( x=-4 \)
\( x=\frac72 \)
The equation has no solution.
1003030101
Level:
A
Solve.
\[ 2^x=-4\]
The equation has no solution.
\( x=2 \)
\( x=-2 \)
\( x=-\frac12 \)
9000003608
Level:
B
Solve the following equation.
\[
\frac{2}
{3}\cdot 9^{x+1} - 13\cdot 6^{x} + 24\cdot 4^{x-1} = 0
\]
\(1,\ -1\)
\(\frac{3}
{2},\ \frac{2}
{3}\)
\(\frac{1}
{2},\ -\frac{1}
{2}\)
\(\frac{3}
{2},\ -\frac{3}
{2}\)
9000003705
Level:
B
Solve the following exponential equation.
\[
3^{2x} - 12\cdot 3^{x} + 27 = 0
\]
\(x_{1} = 1;\ x_{2} = 2\)
\(x_{1} = 3;\ x_{2} = 9\)
\(x_{1} = -1;\ x_{2} = -2\)
\(x_{1} = -3;\ x_{2} = -9\)