2000010308
Level:
A
A sequence has \(n\)th term \(\frac{1}{3+2n}\) . Which term of the sequence is the first to have the value less than \(\frac1{200}\)?
\( a_{99} \)
\( a_{98} \)
\( a_{101} \)
\( a_{102}\)
A
2110010205
Level:
A
Which of the given graphs is the graph of the function \( f(x)=5\cdot 0.2^{-x}\)?
2010010204
Level:
A
In the following list identify a point which is not on the graph of the function
\(f(x) = 4 -\left (\frac{1}
{2}\right )^{x}\).
\(A = [-2;8]\)
\(B =\left [1;\frac72\right]\)
\(C =\left [-1;2\right]\)
\(D =\left [0;3\right]\)
\(E =\left [-3;-4\right]\)
\(F =\left [2;\frac{15}4\right]\)
2010010203
Level:
A
In the following list identify a function whose graph passes through the points
\([2;6]\) and
\([4;14]\).
\(f(x) = \left (\frac{1}
{3}\right )^{2-x} +5\)
\(f(x) = \left (\frac{1}
{3}\right )^{2-x} -5\)
\(f(x) = \left (\frac{1}
{3}\right )^{x-2} -5\)
\(f(x) = 5-\left (\frac{1}
{3}\right )^{x-2} \)
\( f(x)=5+\left(\frac13\right)^{x-2}\)
\( f(x)=5-\left(\frac13\right)^{2-x}\)
2010010104
Level:
A
Solve.
\[ \log_3(x-2)+\log_3x=1 \]
\( x=3 \)
\( x_1=3;\ x_2=-1\)
\( x_1=1;\ x_2=-3 \)
\( x=-3 \)
2010010102
Level:
A
How many solutions in the set of integers does the following equation have?
\[ \log_{2}\!(3x-4)=\log_{2}\!(x-2) \]
no solutions
exactly one solution equal to zero
exactly one negative solution
exactly one positive solution
2010010101
Level:
A
Solve.
\[ \log_3(2x+5)=2\]
\( x=2\)
\( x=7\)
\( x=-\frac32\)
\( x=\frac12\)
2010011008
Level:
A
In the following list identify a positive expression.
\(\log _{0.5}3 -\log _{0.5}48\)
\(\log _{0.5}16 +\log _{0.5}4\)
\(\log _{3}9^3 -\log _{2}4^4\)
\(\log _{5}\left(4^{-1}\right) +\log _{5}\frac4{125}\)
2010011007
Level:
A
In the following list identify the point that is not a point on the graph of the function.
\[f(x)= -2\log _{2}x+3\]
\(\left[\frac12;1\right]\)
\([2;1]\)
\([4;-1]\)
\([1;3]\)
\(\left[\frac18;9\right]\)
\(\left[\frac14;7\right]\)
2010011003
Level:
A
Find the value of \( x \), if
\( \log_{\frac13}x=-4 \).
\( x=81 \)
\( x=\frac1{81} \)
\( x=-81 \)
\( x=\frac1{12} \)