1103136504
Level:
B
What are the values of the real variable \( x \), if \( \log_7x < 0 \)? Use the graph of \( f(x)=\log_7x \) given below.
\( x\in(0;1) \)
\( x\in[1;\infty) \)
\( x\in(0;\infty) \)
\( x\in[0;1] \)
Logarithmic functions
1103136503
Level:
B
What are the values of the real variable \( x \), if \( \log_{0.4}x \leq 0 \)? Use the graph of \( f(x)=\log_{0.4}x \) given below.
\( x\in[1;\infty) \)
\( x\in(0;1] \)
\( x\in(-\infty;0] \)
\( x\in[0;\infty) \)
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.
\( 4 \)
\( 3 \)
\( 2 \)
\( 5 \)
1103136501
Level:
B
Consider the values
\( \log_{0.2}3;\) \(\log_20.3;\) \(\log_{0.3}1;\) \(\log_23;\) \(\log_{\frac32}\frac23;\) \(\log_{\frac23}2;\) \(\log_{0.3}\frac32.\)
Determine how many of the given values are negative. Use the graph of a logarithmic function given below.
\( 5 \)
\( 4 \)
\( 3 \)
\( 2 \)
1103118505
Level:
B
Suppose a logarithmic function \( f \) is unbounded, increasing and \( f \) has an asymptote at \( x=-2 \). Given properties of \( f \), identify a possible graph of this function.
1103118504
Level:
B
Given the next graph of a logarithmic function \( f \), choose the correct list of properties of \( f \).
decreasing, asymptote at \( x=0 \), unbounded
decreasing, asymptote at \( y=0 \), unbounded
decreasing, asymptote at \( x=0 \), bounded below
increasing, asymptote at \( y=0 \), bounded below
1003118503
Level:
B
Which of the following functions is increasing?
\( f\colon y=-\log_{\frac12}x \)
\( f\colon y=-\log_2x \)
\( f\colon y=-2\log_2x \)
\( f\colon y=\log_{\frac12}x \)
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.
1003118501
Level:
B
Given a decreasing logarithmic function \( f(x)=\log_ax \), choose the correct statement about the base \( a \).
\( 0 < a < 1 \)
\( a > 1 \)
\( a=1 \)
\( a < 1 \)
1103099811
Level:
A
Which of the following graphs is the graph of the function \( f(x)=2\log_2x \)?
