1003170903
Level:
C
Find the solution set of the following inequality.
\[ \log_2^2(x-2)< \log_2(x-2) \]
\( (3,4) \)
\( (0,1) \)
\( (-\infty,4) \)
\( (-\infty,1) \)
Logarithmic Equations and Inequalities
1003170902
Level:
C
Find the solution set of the following inequality.
\[ \log_{0.1}\frac{2-x}{x+1}>0 \]
\( \left(\frac12,2\right) \)
\( (-\infty,-1)\cup\left(\frac12,\infty\right) \)
\( \left(-1,\frac12 \right) \)
\( (-1,2) \)
1003170901
Level:
C
Find the solution set of the following inequality.
\[ \log_3\frac{2x-2}{x+3}\leq 0 \]
\( (1,5] \)
\( (-3,5] \)
\( [-3,5] \)
\( [-3,1] \)
1003158805
Level:
B
Which of the following statements about the equation is not true?
\[ \log_{x^2}4+\log_x2+\log_{\frac1x}1=1 \]
The solution is a prime number.
The solution is an even number.
The solution is a positive number.
The solution is an integer.
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.
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.
\[
\log _{0.3}x\geq \log _{0.3}5
\]
\(x\in (0,5] \)
\(x\in (0,\infty )\)
\(x\in (-\infty ,5] \)
\(x\in [ 5,\infty )\)
9000003809
Level:
C
Find the solution set of the following inequality.
\[
\log _{0.5}(x^{2} - 2x) >\log _{
0.5}3
\]
\((-1,0)\cup (2,3)\)
\((-\infty ,0)\cup (2,\infty )\)
\((0,2)\)
\((-\infty ,-1)\cup (0,2)\cup (3,\infty )\)
\((-\infty ,-1)\cup (3,\infty )\)
\((-1,3)\)