2000000603
Level:
A
Which of the following points does not lie on the graph of the function \(f: y=\log_{3}x\)?
\( [3;-1]\)
\( [3;1]\)
\( \left[ \frac{1}{3} ; -1 \right]\)
\( [1;0]\)
A
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.
2000000410
Level:
A
Which of the following equations does not have the solution \(x=-4\)?
\(\log_{3}2x=4\)
\(\log_{2}x^{2}=4\)
\(\log_{x^{2}}16=1\)
\(\log_{x+6}4=2\)
2000000409
Level:
A
Which of the following equations has the solution \(x=2\)?
\(\log_{2x+1}25=2\)
\(1+\log_{x+1}9=2\)
\(\log_{4}x+2=1\)
\(\log_{3}3x=2\)
2000000404
Level:
A
What is the true statement about the solution of the equation
\(\log_{x-1}25=2\)?
It is an even number.
It is a prime number.
It is an odd number.
It is a negative number.
2000000402
Level:
A
Find the solution of the following equation.
\[
\log_{2x-3}x=1
\]
\(x=3\)
\(x=1\)
\(x=0\)
\(x=-3\)
2000000401
Level:
A
Find the solution of the following equation.
\[
\log_{3}(x-9) =2
\]
\(x=18\)
\(x=15\)
\(x=9\)
\(x=0\)
2000000302
Level:
A
Find the solution of the following equation.
\[
\left( \frac{2}{5}\right)^x = 6.25
\]
\( x=-2\)
\( x=2 \)
\( x=-5 \)
\( x=5\)
1003085208
Level:
A
Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_8=\frac83$, $a_k=8$ and the common difference is $\frac23$, find $k$.
$16$
$15$
$14$
$21$
$10$