Logarithmic equations and inequalities

9000003808

Level:

Identify one statement which is true for the following equation. \[ \log (x - 13) -\log (x - 3) = 1 -\log 2 \]

The equation does not have a solution.

The equation has two solutions.

The equation has a unique solution. This solution is a noninteger rational number.

The solution is \(x = 0\).

The equation has a unique solution. This solution is a positive integer.

The equation has a unique solution. This solution is a negative integer.

Level:

Solve the following equation. \[ \log x^{2}\cdot \log \sqrt{x} -\log \frac{1} {x} = 2 \]

\(x_{1} = \frac{1} {100}\), \(x_{2} = 10\)

\(x_{1} = -2\), \(x_{2} = 1\)

\(x_{1} = - \frac{1} {100}\), \(x_{2} = 10\)

\(x_{1} = -1\), \(x_{2} = 2\)

Level:

Find the solution set of the following inequality. \[ \log _{0.5}(x^{2} - 2x) >\log _{ 0.5}3 \]

\((-1;0)\cup (2;3)\)

\((-\infty ;0)\cup (2;\infty )\)

\((0;2)\)

\((-\infty ;-1)\cup (0;2)\cup (3;\infty )\)

\((-\infty ;-1)\cup (3;\infty )\)

\((-1;3)\)