Exponential equations and inequalities

1003030101

Level:

Solve.

2^{x} = - 4

The equation has no solution.

x = 2

x = - 2

x = - \frac{1}{2}

1003030102

Level:

Solve.

5^{8 - 2 x} = 1

x = 4

x = - 4

x = \frac{7}{2}

The equation has no solution.

1003030103

Level:

Solve.

8^{2 x} = 16 \sqrt[3]{4}

x = \frac{7}{9}

x = \frac{11}{12}

x = \frac{4}{9}

x = \frac{1}{3}

1003030104

Level:

Decide which of the following intervals contains

d

, if

{({0.1}^{d - 1})}^{3} = 10^{d - 1}

[- 1; 3]

[9; 13]

[4; 8]

[- 6; - 2]

1003030105

Level:

How many solutions does the following equation have?

\sqrt{81^{x + 1}} = 3^{2 x}

No solutions

Infinitely many solutions

Exactly one solution

Exactly two solutions

1003030106

Level:

How many solutions does the following equation have?

2^{x} \cdot 5^{x} = 100^{3 - x}

Exactly one solution

No solutions

Infinitely many solutions

Exactly two solutions

1003030107

Level:

Solve.

\sqrt[2 x + 6]{9^{x + 2}} = \sqrt[6]{243}

x = 3

x = - 8

x = \frac{- 24}{7}

x = - 3

1003044501

Level:

Identify the solution of the equation.

2^{x^{2} - x - 3} = 8.

x_{1} = 3

x_{2} = - 2

x_{1} = - 3

x_{2} = 2

x_{1} = 0

x_{2} = 1

x_{1} = 0

x_{2} = - 1

1003044502

Level:

The following exponential equation has solutions

x_{1}

and

x_{2}

. Find the sum of

x_{1}

and

x_{2}

\frac{4^{x^{2}}}{16^{x + 1}} = 16 \cdot 4^{x}

3

- 3

- 1

2

1003044503

Level:

Identify the solution of the equation.

3^{x - 3} - 3^{x - 2} = 2

The equation has no solution.

x = 3

x = - 3

x = 2

Exponential equations and inequalities

1003030101

1003030102

1003030103

1003030104

1003030105

1003030106

1003030107

1003044501

1003044502

1003044503

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