1003030107
Level:
A
Solve.
\[ \sqrt[2x+6]{9^{x+2}}=\sqrt[6]{243}\]
\( x=3 \)
\( x=-8 \)
\( x=\frac{-24}7 \)
\( x=-3 \)
Exponential equations and inequalities
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.
\( x=2 \)
\( x=-2 \)
\( x=-\frac12 \)
9000003604
Level:
B
Solve the following equation.
\[
10^{x} - 5^{x-1}\cdot 2^{x-2} = 950
\]
\(x = 3\)
\(x = 1\)
\(x = 2\)
\(x = 4\)
9000003609
Level:
C
Solve the following inequality.
\[
\left (\frac{3}
{4}\right )^{x^{2}-2x
}\leq \frac{4^{x-6}}
{3^{x-6}}
\]
\(x\in (-\infty ;-2] \cup [ 3;\infty )\)
\(x\in \mathbb{R}\setminus \{ - 2;3\}\)
\(x\in \mathbb{R}\setminus \{ - 3;2\}\)
\(x\in [ - 2;3] \)
9000003709
Level:
C
Solve the following inequality.
\[
\left (\frac{2}
{3}\right )^{2-3x} < \frac{2^{x+1}}
{3^{x+1}}
\]
\(\left (-\infty ; \frac{1}
{4}\right )\)
\(\left (-\frac{1}
{4};\infty \right )\)
\((-\infty ;4)\)
\(\left (\frac{1}
{4};\infty \right )\)
\((4;\infty )\)
\(\left (-\infty ;-\frac{1}
{4}\right )\)