Logarithmic equations and inequalities

1003138509

Level:

Solve.

\log_{2} (x - 1) + \log_{2} x = 1

x = 2

x_{1} = - 1; x_{2} = 2

x_{1} = - 2; x_{2} = 1

x = 1

1003138508

Level:

How many solutions does the following equation have?

2 \log x^{4} - \log x^{5} - 3 \log x^{3} = 12

exactly one positive solution

exactly one negative solution

exactly one integer solution

no solutions

1003138507

Level:

Solve.

\log_{4} x = 2 - \log_{4} 8

x = 2

x = 1

x = 0

The equation has no solution.

1003138506

Level:

Solve.

\frac{\log_{3} x - 3}{3 + \log_{3} x} = 0

x = 27

x = 9

x_{1} = \frac{1}{27}; x_{2} = 27

infinitely many solutions

1003138505

Level:

Solve.

\ln (- 2 x - 6) = \ln (- 3 x - 9)

The equation has no solution.

x = - 3

x = 3

x = - 15

1003138504

Level:

Solve.

\log_{3} (- 5 x - 2) = \log_{3} (x - 4)

The equation has no solution.

x = \frac{1}{3}

x = 3

x = \frac{3}{2}

1003138503

Level:

How many solutions in the set of integers does the following equation have?

\log_{\frac{1}{2}} (x + 6) = \log_{\frac{1}{2}} (3 x - 6)

exactly one positive solution

exactly one negative solution

exactly one solution equal to zero

no solutions

1003138502

Level:

Solve.

\log_{\frac{1}{3}} (3 - x) = 0

x = 2

The equation has no solution.

x = 3

x = - 4

1003138501

Level:

Solve.

\log_{2} (3 x - 5) = 4

x = 7

x = 3

x = \frac{11}{3}

x = - \frac{1}{3}

1003177802

Level:

Choose the domain of the expression

\ln (- | 3 - 2 x | + 6)

(- \frac{3}{2}; \frac{9}{2})

(- \infty; - \frac{3}{2}) \cup (\frac{9}{2}; \infty)

(- \infty; \frac{3}{2}) \cup (\frac{9}{2}; \infty)

(\frac{9}{2}; \infty)

Logarithmic equations and inequalities

1003138509

1003138508

1003138507

1003138506

1003138505

1003138504

1003138503

1003138502

1003138501

1003177802

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