2000014105
Level:
C
Find the value of \( \left( \log_{\frac1a}b\right) \cdot \left( \log_{\frac1b}c\right) \cdot \left( \log_{\frac1c}a\right)\).
\( -1\)
\( \frac1{abc}\)
\( abc\)
\( 1\)
Calculations with logarithms
2000014104
Level:
C
Find the value of \(L\) if \(L=\log_{\sqrt{2}}2 \cdot \log_2 \sqrt{3} \cdot \log_{\sqrt{3}} 4\).
\( L=4\)
\( L=2\)
\( L=3\)
\( L=1\)
2000014103
Level:
C
Find the value of \( \log_{ab}x\) if \(\log_a x=2\) and \(\log_b x=3\).
\( \frac65\)
\( \frac16\)
\( 6\)
\( \frac56\)
2010011005
Level:
B
If \( a \), \( b \), \( c\in(0;\infty) \) then the expression \( \log_2a+3 \log_2 b-\frac12 \log_2c \) is equivalent to:
\( \log_2\frac{ab^3}{\sqrt{c}} \)
\( \log_2\frac{3ab}{\frac12 c} \)
\( \log_2 \left({ab^3}{c}^{\frac12} \right)\)
\( \log_2 \left(-\frac32 abc\right) \)
2010011004
Level:
C
If \( x\in(0;1)\cup(1;\infty) \) then the product \( \left(\log_x4\right)\left(\log_{16}x\right) \) can be written as:
\( \frac12 \)
\( 2 \)
\( \log_x 4 + \log_{16} x \)
\( \frac1{4} \)
2010011003
Level:
A
Find the value of \( x \), if
\( \log_{\frac13}x=-4 \).
\( x=81 \)
\( x=\frac1{81} \)
\( x=-81 \)
\( x=\frac1{12} \)
2010011002
Level:
A
Which of the following statements is not true?
\( \log_{\frac12}6=-3 \)
\( \log_{\frac12}8=-3\)
\( \log_2 \sqrt{2}=\frac12\)
\( \log_{\frac12}\frac14=2\)
2010011001
Level:
A
Among offered answers, choose a logarithmic form of the following equality.
\[ \sqrt{16} = 4 \]
\( \log_{16}4=\frac{1}{2}\)
\( \log_{\frac12}16=4\)
\( \log_4 \frac12=16\)
\( \log_{2}4=16\)
2000000606
Level:
A
The value of the expression \(3\log_{4}2 - \frac{1}{2}\log_{4}16\) is:
\(0.5\)
\(2\)
\(\log_{4}\frac{9}{256}\)
\( \frac{3}{2} \log_{4}\frac{1}{8}\)
1003102415
Level:
C
Let \( a \in(0;\infty) \). The expression \( \log_4a-\log_{16}a-\log_{\frac14}a \) is equivalent to:
\( \frac32 \log_4a \)
\( -\frac12\log_4a \)
\( \log_4a \)
\( 0 \)