1003102401
Level:
A
Among offered answers, choose a logarithmic form of the following equality.
\[ 8^2 = 64 \]
\( \log_864=2 \)
\( \log_264=8 \)
\( \log_82=64 \)
\( \log_28=64 \)
Calculations with logarithms
1003102402
Level:
A
Find the value of \( y \) if
\[ \log_42=y. \]
\( y=\frac12 \)
\( y=-1 \)
\( y=2 \)
\( y=1 \)
1003102403
Level:
A
Find the value of \( x \) if
\[ \log_x8=-3. \]
\( x=\frac12 \)
\( x=2 \)
\( x=\sqrt2 \)
\( x=-\frac12 \)
1003102404
Level:
A
Which of the following statements is not true?
\( \log_{\sqrt2}2=\frac12 \)
\( \log_{\frac12}2=-1 \)
\( \log_21= 0 \)
\( \log_2\sqrt2=\frac12 \)
1003102405
Level:
A
If \( \log_x\frac49=-\frac12 \) then \( x \) is equal to:
\( \frac{81}{16} \)
\( \frac{16}{81} \)
\( \frac23 \)
\( -\frac23 \)
1003102406
Level:
A
Find the value of \( z \), if
\( \log_3z=-3 \).
\( z=\frac1{27} \)
\( z=27 \)
\( z=-9 \)
\( z=\frac19 \)
1003102408
Level:
A
The value of the expression \( \log_{16}\left(\log_216 \right) \) is:
\( \frac12 \)
\( \frac14 \)
\( \frac18 \)
\( 2 \)
2000000606
Level:
A
The value of the expression \(3\log_{4}2 - \frac{1}{2}\log_{4}16\) is:
\(0.5\)
\(2\)
\(\log_{4}\frac{9}{256}\)
\( \frac{3}{2} \log_{4}\frac{1}{8}\)
2000014110
Level:
A
Identify which of the following equalities is not equivalent to the equality \(4^x=9\).
\( x=2\log_2 9\)
\( x=\log_2 3\)
\( x=\log_4 9\)
\( x=2\log_4 3\)
2010011001
Level:
A
Among offered answers, choose a logarithmic form of the following equality.
\[ \sqrt{16} = 4 \]
\( \log_{16}4=\frac{1}{2}\)
\( \log_{\frac12}16=4\)
\( \log_4 \frac12=16\)
\( \log_{2}4=16\)