1003158804
Level:
B
Which of the following statements is not true about the equation?
\[ \log_x16+\log_{\frac1x}4=2 \]
The solution is an odd number.
The solution is \( x=2 \).
The solution is an even number.
The solution is a prime number.
Logarithmic equations and inequalities
1003158803
Level:
B
Solve
\[ \log_{\frac12}(x)+2=3\log_2(x) \text{ .} \]
\( x=\sqrt2 \)
\( x=2 \)
\( x=-1 \)
Equation has no solution.
1003158802
Level:
B
Find the solution set of the following equation.
\[ \log_{0.2}(x)-4\log_{0.04}(x)=\log_5(x) \]
\( (0;\infty) \)
\( \mathbb{R} \)
\( \emptyset \)
\( [ 0;\infty) \)
1003158801
Level:
B
Solve
\[ \log_2(x)-\log_4(x)=1\text{ .} \]
\( x=4 \)
\( x=2 \)
\( x_1=\frac12\text{, }x_2=4 \)
\( x_1=-1\text{, }x_2=2 \)
9000004901
Level:
C
Solve the following inequality.
\[
\log _{0.3}x\geq \log _{0.3}5
\]
\(x\in (0;5] \)
\(x\in (0;\infty )\)
\(x\in (-\infty ;5] \)
\(x\in [ 5;\infty )\)
9000003806
Level:
B
In the following list identify an equation such that neither
\(x = 5\) nor
\(x = 3\) is the
solution of this equation.
\(\log _{3}(1 - x) =\log _{3}(x + 16 - x^{2})\)
\(\log (54 - x^{3}) = 3\cdot \log x\)
\(\log _{5}(x^{2} - 17) =\log _{5}(x + 3)\)
\(\log (x - 2) -\log (4 - x) = 1 -\log (13 - x)\)
9000003808
Level:
B
Identify one statement which is true for the following equation.
\[
\log (x - 13) -\log (x - 3) = 1 -\log 2
\]
The equation does not have a solution.
The equation has two solutions.
The equation has a unique solution. This solution is a noninteger rational
number.
The solution is \(x = 0\).
The equation has a unique solution. This solution is a positive integer.
The equation has a unique solution. This solution is a negative integer.
9000003805
Level:
B
Solve the following equation.
\[
\log x^{2}\cdot \log \sqrt{x} -\log \frac{1}
{x} = 2
\]
\(x_{1} = \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = 1\)
\(x_{1} = - \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -1\),
\(x_{2} = 2\)
9000003809
Level:
C
Find the solution set of the following inequality.
\[
\log _{0.5}(x^{2} - 2x) >\log _{
0.5}3
\]
\((-1;0)\cup (2;3)\)
\((-\infty ;0)\cup (2;\infty )\)
\((0;2)\)
\((-\infty ;-1)\cup (0;2)\cup (3;\infty )\)
\((-\infty ;-1)\cup (3;\infty )\)
\((-1;3)\)