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.
Logarithmic equations and inequalities
2010010104
Level:
A
Solve.
\[ \log_3(x-2)+\log_3x=1 \]
\( x=3 \)
\( x_1=3;\ x_2=-1\)
\( x_1=1;\ x_2=-3 \)
\( x=-3 \)
2010010103
Level:
B
Solve
\[ \frac{\log(x^2+7)}{\log(x+7)}=\frac{\log{25}}{\log5} \text{ .} \]
\( x=-3 \)
\( x=-5 \)
\( x_1=3;\ x_2=-3 \)
\( x=-2 \)
2010010102
Level:
A
How many solutions in the set of integers does the following equation have?
\[ \log_{2}\!(3x-4)=\log_{2}\!(x-2) \]
no solutions
exactly one solution equal to zero
exactly one negative solution
exactly one positive solution
2010010101
Level:
A
Solve.
\[ \log_3(2x+5)=2\]
\( x=2\)
\( x=7\)
\( x=-\frac32\)
\( x=\frac12\)
2000000505
Level:
B
Find the number which satisfies the following equation.
\[
4^x =9
\]
\(x=2\log_{4}3\)
\(x=\frac{\log{2}}{\log 3}\)
\(x=2\log_{9}2\)
\(x=\log 9 - \log 4\)
2000000410
Level:
A
Which of the following equations does not have the solution \(x=-4\)?
\(\log_{3}2x=4\)
\(\log_{2}x^{2}=4\)
\(\log_{x^{2}}16=1\)
\(\log_{x+6}4=2\)
2000000409
Level:
A
Which of the following equations has the solution \(x=2\)?
\(\log_{2x+1}25=2\)
\(1+\log_{x+1}9=2\)
\(\log_{4}x+2=1\)
\(\log_{3}3x=2\)
2000000408
Level:
B
Find the solution of the following equation.
\[
4^{\log_{2}x}=1
\]
\(x=1\)
\(x=-1\)
\(x=\frac{1}{2}\)
\(x=2\)
2000000407
Level:
C
Which number belongs to the set of all solutions of the inequality \(\log_{x}4< 2\)?
\(x=\sqrt{8}\)
\(x=-2\)
\(x=2\)
\(x=\sqrt{2}\)