2010011002
Level:
A
Which of the following statements is not true?
\( \log_{\frac12}6=-3 \)
\( \log_{\frac12}8=-3\)
\( \log_2 \sqrt{2}=\frac12\)
\( \log_{\frac12}\frac14=2\)
Calculations with logarithms
2010011003
Level:
A
Find the value of \( x \), if
\( \log_{\frac13}x=-4 \).
\( x=81 \)
\( x=\frac1{81} \)
\( x=-81 \)
\( x=\frac1{12} \)
2010016007
Level:
A
If \(\log_3 a=b\) then the value of \(\log_9 a\) is equal to:
\(\frac{b}2\)
\(2b\)
\( \frac2{b}\)
\(9b\)
2010016008
Level:
A
If \(\log_2 a=b\) then the value of \(\log_8 a\) is equal to:
\(\frac{b}3\)
\(\frac{b}2\)
\(3b\)
\(4b\)
9000022802
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\log \left (2x^{2} + 4x - 6\right )
\]
\(\left [ -3;1\right ] \)
\(\left (-\infty ;-3\right )\cup \left (1;\infty \right )\)
\(\left (-3;1\right )\)
\(\left (-\infty ;-3\right ] \cup \left [ 1;\infty \right )\)
9000034902
Level:
A
Find the domain of the following expression.
\[
\log _{2}\left [\left (\frac{2}
{3} - x\right )\left (x + \frac{1}
{4}\right )\right ]
\]
\(\left (-\frac{1}
{4}; \frac{2}
{3}\right )\)
\(\left (-\infty ;-\frac{1}
{4}\right ] \cup \left [ \frac{2}
{3};\infty \right )\)
\(\left (-\infty ;-\frac{1}
{4}\right )\cup \left (\frac{2}
{3};\infty \right )\)
\(\left [ \frac{1}
{4}; \frac{2}
{3}\right ] \)
9000034904
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\log _{\frac{1}
{4} }\left [\left (x + \frac{1}
{2}\right )\left (5 - 2x\right )\right ]
\]
\(\left (-\infty ;-\frac{1}
{2}\right ] \cup \left [ \frac{5}
{2};\infty \right )\)
\(\left [ -\frac{1}
{2}; \frac{5}
{2}\right ] \)
\(\left (-\frac{1}
{2}; \frac{5}
{2}\right )\)
\(\left (-\infty ;-\frac{1}
{2}\right )\cup \left (\frac{5}
{2};\infty \right )\)
1003102409
Level:
B
Without a calculator evaluate the following expression and select the correct value.
\[ \log_64+\log_69 \]
\( 2 \)
\( 36 \)
\( 13 \)
\( 6 \)
1003102411
Level:
B
Without a calculator evaluate the following expression and select the correct value.
\[ \frac{\log\sqrt6}{\log6} \]
\( \frac12 \)
\( 2 \)
\( \frac{\sqrt6}6 \)
\( \sqrt6-6 \)
1003102412
Level:
B
If \( a \), \( b \), \( c\in(0;\infty) \) then the expression \( \log_5a-\frac23 \log_5 b+3\log_5c \) is equivalent to:
\( \log_5\frac{ac^3}{\sqrt[3]{b^2}} \)
\( \log_5\frac{a\sqrt[3]{b^2}}{c^3} \)
\( \log_5\frac{3ac}{\frac23 b} \)
\( \log_5\frac{\frac23 ab}{3c} \)