2010016008
Level:
A
If \(\log_2 a=b\) then the value of \(\log_8 a\) is equal to:
\(\frac{b}3\)
\(\frac{b}2\)
\(3b\)
\(4b\)
Calculations with logarithms
2010016007
Level:
A
If \(\log_3 a=b\) then the value of \(\log_9 a\) is equal to:
\(\frac{b}2\)
\(2b\)
\( \frac2{b}\)
\(9b\)
2010016004
Level:
B
The number \( \log_3 6 -1\) equals:
\(\log_3 2\)
\( \log_3 5\)
\( 5\)
\( 1\)
2010016003
Level:
B
The number \( 1+\log_2 7\) equals:
\(\log_2 14\)
\( 3\)
\( 4.5\)
\( \log_2 9\)
2010016002
Level:
B
The value of the expression \( \log 125^2+\log 8^2\) is:
\(6\)
\( 5\)
\( 4+\log 133\)
\( 8+\log 133\)
2010016001
Level:
B
The value of the expression \( \log 25^4+\log 4^4\) is:
\(8\)
\( 4\)
\( 4+\log 29\)
\( 8+\log 29\)
2000014110
Level:
A
Identify which of the following equalities is not equivalent to the equality \(4^x=9\).
\( x=2\log_2 9\)
\( x=\log_2 3\)
\( x=\log_4 9\)
\( x=2\log_4 3\)
2000014108
Level:
C
Find the value of \(\log_{y^2x}y^7x^5\) if \(\log_x y=-2\).
\( 3\)
\( -3\)
\( 17.5\)
\( \frac{17}3\)
2000014107
Level:
C
Choose the correct equality.
\( 4^{\log_23}=9\)
\( 2^{1-\log_23}=3\)
\( 4^{\log_24}=4\)
\( 4^{1+\log_42}=16\)
2000014106
Level:
B
Find the value of \( \log_2 5 + \log_2 20\) if \(\log_2 5=a\) and \( \log_2 20=b\).
\( 2a+2\)
\( 2^a+2^b\)
\( ab\)
\( 5a\)