Calculations with logarithms

1003102405

Level:

\log_{x} \frac{4}{9} = - \frac{1}{2}

then

x

is equal to:

\frac{81}{16}

\frac{16}{81}

\frac{2}{3}

- \frac{2}{3}

Level:

Which of the following statements is not true?

\log_{\sqrt{2}} 2 = \frac{1}{2}

\log_{\frac{1}{2}} 2 = - 1

\log_{2} 1 = 0

\log_{2} \sqrt{2} = \frac{1}{2}

Level:

Find the value of

x

\log_{x} 8 = - 3.

x = \frac{1}{2}

x = 2

x = \sqrt{2}

x = - \frac{1}{2}

Level:

Find the value of

y

\log_{4} 2 = y .

y = \frac{1}{2}

y = - 1

y = 2

y = 1

Level:

Among offered answers, choose a logarithmic form of the following equality.

8^{2} = 64

\log_{8} 64 = 2

\log_{2} 64 = 8

\log_{8} 2 = 64

\log_{2} 8 = 64

Level:

Find the domain of the following expression.

\log_{2} [(\frac{2}{3} - x) (x + \frac{1}{4})]

(- \frac{1}{4}; \frac{2}{3})

(- \infty; - \frac{1}{4}] \cup [\frac{2}{3}; \infty)

(- \infty; - \frac{1}{4}) \cup (\frac{2}{3}; \infty)

[\frac{1}{4}; \frac{2}{3}]

Level:

Find all

x \in R

for which the following expression is undefined.

\log_{\frac{1}{4}} [(x + \frac{1}{2}) (5 - 2 x)]

(- \infty; - \frac{1}{2}] \cup [\frac{5}{2}; \infty)

[- \frac{1}{2}; \frac{5}{2}]

(- \frac{1}{2}; \frac{5}{2})

(- \infty; - \frac{1}{2}) \cup (\frac{5}{2}; \infty)

Level:

Find all

x \in R

for which the following expression is undefined.

\log (2 x^{2} + 4 x - 6)

[- 3; 1]

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

(- 3; 1)

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