2010010101
Level:
A
Solve.
\[ \log_3(2x+5)=2\]
\( x=2\)
\( x=7\)
\( x=-\frac32\)
\( x=\frac12\)
Logarithmic equations and inequalities
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 \(\log_{x}4< 2\)?
\(x=\sqrt{8}\)
\(x=-2\)
\(x=2\)
\(x=\sqrt{2}\)
2000000406
Level:
C
Which number does not belong to the set of all solutions of the inequality \(\log_{2x}(x+2)< 1\)?
\(x=2\)
\(x=3\)
\(x=4\)
\(x=5\)
2000000405
Level:
C
Which number belongs to the set of all solutions of the inequality \(\log_{2x-2}x< 1\)?
\(x=3\)
\(x=1\)
\(x=0\)
\(x=0.5\)
2000000404
Level:
A
What is the true statement about the solution of the equation
\(\log_{x-1}25=2\)?
It is an even number.
It is a prime number.
It is an odd number.
It is a negative number.
2000000403
Level:
B
Find the solution of the following equation.
\[
\log_{3}(\log_{3}x)=0
\]
\(x=3\)
\(x=1\)
\(x=27\)
\(x=9\)