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1003158805

Level:

Which of the following statements about the equation is not true? \[ \log_{x^2}4+\log_x2+\log_{\frac1x}⁡1=1 \]

The solution is a prime number.

The solution is an even number.

The solution is a positive number.

The solution is an integer.

1003158804

Level:

Which of the following statements is not true about the equation? \[ \log_x⁡16+\log_{\frac1x}⁡4=2 \]

The solution is an odd number.

The solution is $ x=2 $.

The solution is an even number.

The solution is a prime number.

1003158803

Level:

Solve \[ \log_{\frac12}⁡(x)+2=3\log_2⁡(x) \text{ .} \]

$ x=\sqrt2 $

$ x=2 $

$ x=-1 $

Equation has no solution.

1003158802

Level:

Find the solution set of the following equation. \[ \log_{0.2}(x)-4\log_{0.04}⁡(x)=\log_5⁡(x) \]

$ (0,\infty) $

$ \mathbb{R} $

$ \emptyset $

$ [ 0,\infty) $

1003158801

Level:

Solve \[ \log_2⁡(x)-\log_4⁡(x)=1\text{ .} \]

$ x=4 $

$ x=2 $

$ x_1=\frac12\text{, }x_2=4 $

$ x_1=-1\text{, }x_2=2 $

We were given an oscillating sequence $ 3\text{, }-3\text{, }\ 3\text{, }-3\text{, }\ 3\dots $ (numbers $ 3 $ and $ -3 $ alternate regularly). What is the formula for the $n$th element of the sequence?

$ a_n=(-1)^{n+1}\cdot3\text{, }\ n\in\mathbb{N} $

$ a_n=(-1)^{n}\cdot3\text{, }\ n\in\mathbb{N} $

$ a_n=3^n\text{, }\ n\in\mathbb{N} $

$ a_n=-3^n\text{, }\ n\in\mathbb{N} $

1003124909

Level:

The number $ \frac1{2^{2015}}\cdot(0.0005)^{2015} $ equals:

$ (0.00025)^{2015} $

$ \frac1{2000^{2015}} $

$ (0.001)^{2015} $

$ (0.0025)^{2015} $

1003124908

Level:

Half the inverse of the cube of the number $ 8^{19} $ is:

$ 4^{-86} $

$ 2^{170} $

$ \frac1{8^{57}} $

$ \frac1{2^{170}} $

1003124907

Level:

The multiplicative inverse of the number $ \frac{\sqrt[3]{27^2}:9^{\frac12}}{\sqrt[3]9} $ is:

$ 3^{-\frac13} $

$ 3^{\frac23} $

$ 3^{\frac13} $

$ 3^{-\frac23} $

1003124901

Level:

The fraction $ \frac{1+\sqrt3}{3+\sqrt{11}} $ is equal to:

$ \frac{\sqrt{11}-3}{\sqrt3-1}$

$ 9 $

$ \frac{\sqrt{11}-3}{1-\sqrt3} $

$ \frac{\sqrt{11}+2\sqrt3}2 $

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