2010011007
Level:
A
In the following list identify the point that is not a point on the graph of the function.
\[f(x)= -2\log _{2}x+3\]
\(\left[\frac12;1\right]\)
\([2;1]\)
\([4;-1]\)
\([1;3]\)
\(\left[\frac18;9\right]\)
\(\left[\frac14;7\right]\)
Logarithmic functions
2010011006
Level:
C
Find the domain of the following function.
\[
f(x)= \log\left( \log_{\frac1{10}}\left(1-x^2\right)\right)
\]
\( (-1 ;0) \cup (0;1)\)
\( (-1 ;1)\)
\( (0;1)\)
\([ 0;1)\)
\((-\infty;1)\)
2000000607
Level:
A
In how many points do the graphs of \(f:y=-x+1\) and \(g:y=\log_{2}x\) intersect?
\(1\)
\(0\)
\(2\)
\(3\)
2000000605
Level:
A
Which of the following sets is the domain of the function \(f: y=\log(x^2+9)\)?
\( \mathbb{R}\)
\( (-\infty;-3) \cup (3;+\infty)\)
\( (-3;3)\)
\( \mathbb{R} \setminus \{-3;3\}\)
2000000604
Level:
A
Which number does not belong to the domain of the function \(f: y=\log(x^2-4)\)?
\(x=\sqrt{3}\)
\(x=-\sqrt{5}\)
\(x=4\)
\(x=-\sqrt{6}\)
2000000603
Level:
A
Which of the following points does not lie on the graph of the function \(f: y=\log_{3}x\)?
\( [3;-1]\)
\( [3;1]\)
\( \left[ \frac{1}{3} ; -1 \right]\)
\( [1;0]\)
2000000602
Level:
A
The graph of which of the following functions contains the point \( \left[ \frac{1}{4} ; -1 \right]\)?
\(f:y=\log_{4}x\)
\(f:y=\log_{\frac{1}{2}}x\)
\(f:y=\log_{2}x\)
\(f:y=\log_{\frac{1}{4}}x\)
2000000601
Level:
A
The graph of \(f\colon y=\log_{2}x+2\) is obtained from the graph of \(g\colon y=\log_{2}x\) by shifting the graph of \(g\) by:
\(2\) units up.
\(2\) units down.
\(2\) units right.
\(2\) units left.
Rewriting Logarithmic Equations to Exponential Form
Submitted by ladislav.foltyn on Sat, 02/23/2019 - 14:39Question:
Given a logarithmic equation, choose its equivalent exponential form.
Properties of Logarithmic Functions
Submitted by ladislav.foltyn on Fri, 02/15/2019 - 15:28Question:
Let
\begin{align*} f(x)&=\log_5x\text{ ,}\quad &g(x)&=\log_{\frac12}(x+1)\text{ ,}\quad &h(x)&=\log_2(x)+1\text{ ,}\\ k(x)&=\log_{\frac14}(x-1)+1\text{ ,}\quad &l(x)&=-\log_3(-x)\text{ ,}\quad &m(x)&=\log_3(1-x)+1\text{ .} \end{align*}
In the table, at each line, choose the functions for which the statement is true.