1003102404
Level:
A
Which of the following statements is not true?
\( \log_{\sqrt2}2=\frac12 \)
\( \log_{\frac12}2=-1 \)
\( \log_21= 0 \)
\( \log_2\sqrt2=\frac12 \)
Calculations with logarithms
1003102403
Level:
A
Find the value of \( x \) if
\[ \log_x8=-3. \]
\( x=\frac12 \)
\( x=2 \)
\( x=\sqrt2 \)
\( x=-\frac12 \)
1003102402
Level:
A
Find the value of \( y \) if
\[ \log_42=y. \]
\( y=\frac12 \)
\( y=-1 \)
\( y=2 \)
\( y=1 \)
1003102401
Level:
A
Among offered answers, choose a logarithmic form of the following equality.
\[ 8^2 = 64 \]
\( \log_864=2 \)
\( \log_264=8 \)
\( \log_82=64 \)
\( \log_28=64 \)
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.
\[
\log _{\frac{1}
{4} }\left [\left (x + \frac{1}
{2}\right )\left (5 - 2x\right )\right ]
\]
\(\left (-\infty ;-\frac{1}
{2}\right ] \cup \left [ \frac{5}
{2};\infty \right )\)
\(\left [ -\frac{1}
{2}; \frac{5}
{2}\right ] \)
\(\left (-\frac{1}
{2}; \frac{5}
{2}\right )\)
\(\left (-\infty ;-\frac{1}
{2}\right )\cup \left (\frac{5}
{2};\infty \right )\)
9000022802
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\log \left (2x^{2} + 4x - 6\right )
\]
\(\left [ -3;1\right ] \)
\(\left (-\infty ;-3\right )\cup \left (1;\infty \right )\)
\(\left (-3;1\right )\)
\(\left (-\infty ;-3\right ] \cup \left [ 1;\infty \right )\)
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