9000004904
Level:
A
In the following list identify a function with a domain
\(\left (-\infty ; \frac{2}
{3}\right ).\)
\(y =\log (2 - 3x)\)
\(y =\log (3x - 2)\)
\(y = -\log (3x - 2)\)
\(y =\log (2x - 3)\)
\(y =\log (3 - 2x)\)
none of the above
Logarithmic functions
9000004906
Level:
A
Identify a possible analytic expression for the function
\(f\)
graphed in the picture.
\(y =\log _{2}x\)
\(y =\log _{0.2}x\)
\(y =\log _{0.5}x\)
\(y =\log _{5}x\)
9000004909
Level:
A
Identify a possible analytic expression for the function
\(g\)
graphed in the picture.
\(y =\log _{3}(x + 2) - 1\)
\(y =\log _{\frac{1}
{3} }(x + 2) - 1\)
\(y =\log _{3}(x - 2) + 1\)
\(y =\log _{\frac{1}
{3} }(x - 2) + 1\)
9100004907
Level:
A
Identify a possible graph of the function
\(f\colon y =\log _{0.2}x\).
1003118501
Level:
B
Given a decreasing logarithmic function \( f(x)=\log_ax \), choose the correct statement about the base \( a \).
\( 0 < a < 1 \)
\( a > 1 \)
\( a=1 \)
\( a < 1 \)
1003118502
Level:
B
Given a function \( f(x)=b\cdot \log_ax \), where \( a > 1 \) and \( b < 0 \), find the correct statement.
Function \( f \) is decreasing.
Function \( f \) is increasing.
Function \( f \) is bounded.
Function \( f \) is bounded below.
1003118503
Level:
B
Which of the following functions is increasing?
\( f\colon y=-\log_{\frac12}x \)
\( f\colon y=-\log_2x \)
\( f\colon y=-2\log_2x \)
\( f\colon y=\log_{\frac12}x \)
1003136502
Level:
B
Consider the values
\(\ \log_74;\) \(\log_{\frac47}{0.4};\) \(\log_40.7;\) \(\log_{\frac74}4;\) \(\log_{0.7}0.4;\) \(\log_{0.4}4;\) \(\log_7{0.7}.\ \)
Without using a calculator, determine how many of the given values are positive.
\( 4 \)
\( 3 \)
\( 2 \)
\( 5 \)
1003136507
Level:
B
What are the values of the real parameter \( a \), that satisfy inequality \( \log_a\frac47 > \log_a \frac74 \)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)
1003136508
Level:
B
What are the values of the real parameter \( a \), that satisfy inequality \( \log_a7 < \log_a4 \)?
\( 0 < a < 1 \)
\( a > 1 \)
\( a < 1 \)
\( a > 0 \)