2000000403
Level:
B
Find the solution of the following equation.
\[
\log_{3}(\log_{3}x)=0
\]
\(x=3\)
\(x=1\)
\(x=27\)
\(x=9\)
Logarithmic equations and inequalities
2000000408
Level:
B
Find the solution of the following equation.
\[
4^{\log_{2}x}=1
\]
\(x=1\)
\(x=-1\)
\(x=\frac{1}{2}\)
\(x=2\)
2000000505
Level:
B
Find the number which satisfies the following equation.
\[
4^x =9
\]
\(x=2\log_{4}3\)
\(x=\frac{\log{2}}{\log 3}\)
\(x=2\log_{9}2\)
\(x=\log 9 - \log 4\)
2000011301
Level:
B
Let \( x \in (0;1) \cup (1;+\infty)\). Find the value of \(m \in \mathbb{R}\) if \(2\log_m x=\frac32 \log_2 x\).
\(m=2^{\frac43}\)
\(m=2^{\frac34}\)
\(m={\frac34}\)
\(m={\frac43}\)
2000011302
Level:
B
Find the solution of the equation \(\log_{16}x+\log_4x+\log_2x=7\).
\(x=16\)
\(x=4\)
\(x={\frac12}\)
\(x=2\)
2010010103
Level:
B
Solve
\[ \frac{\log(x^2+7)}{\log(x+7)}=\frac{\log{25}}{\log5} \text{ .} \]
\( x=-3 \)
\( x=-5 \)
\( x_1=3;\ x_2=-3 \)
\( x=-2 \)
2010010105
Level:
B
Solve.
\[ 3^{2x}=5 \]
\( x=\frac12 \log_3 5 \)
\( x=2 \log_3 5 \)
\( x= \log_3 {5^2} \)
The equation has no solution.
2010010106
Level:
B
Which of the following statements about the given equation is true?
\[ \log_2(x-2)^2=4-\frac2{\log_2(x-2)} \]
The equation has exactly one solution.
The solution set consists of two prime numbers.
The solution set is the empty set.
None of the above statements is true.
2010010107
Level:
B
Solve the following equation.
\[
\log_2 x^{3}\cdot \log_2 \sqrt[3]{x} +\log_2 \frac{1}
{x} = 6
\]
\(x_{1} = 8\),
\(x_{2} = \frac14\)
\(x_{1} = 2\),
\(x_{2} = 3\)
\(x_{1} = -8\),
\(x_{2} = -\frac14\)
\(x_{1} = \frac18\),
\(x_{2} = 4\)
9000003805
Level:
B
Solve the following equation.
\[
\log x^{2}\cdot \log \sqrt{x} -\log \frac{1}
{x} = 2
\]
\(x_{1} = \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = 1\)
\(x_{1} = - \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -1\),
\(x_{2} = 2\)