Logarithmic functions

1103138402

Level:

From the following functions choose the one which is graphed in the picture.

k (x) = \log_{2} | x |

m (x) = | \log_{2} x |

f (x) = \log_{2} \sqrt{x}

g (x) = \sqrt{\log_{2} x}

1103138401

Level:

From the following functions choose the one which is graphed in the picture.

f (x) = | \log_{\frac{1}{2}} x |

g (x) = \log_{\frac{1}{2}} | x |

k (x) = \log_{\frac{1}{2}} \sqrt{x}

m (x) = \sqrt{\log_{\frac{1}{2}} x}

1003136511

Level:

Identify which of the following relations is correct.

\log_{2} 8 > \log_{2} \frac{7}{2} > \log_{2} 1 > \log_{2} \frac{4}{7} > \log_{2} \frac{1}{7}

\log_{2} \frac{1}{7} > \log_{2} \frac{4}{7} > \log_{2} 1 > \log_{2} \frac{7}{4} > \log_{2} 8

\log_{2} 8 > \log_{2} \frac{7}{4} > \log_{2} \frac{4}{7} > \log_{2} \frac{1}{7} > \log_{2} 1

\log_{2} 8 > \log_{2} \frac{7}{4} > \log_{2} \frac{4}{7} > \log_{2} 1 > \log_{2} \frac{1}{7}

1103136510

Level:

Identify which of the following relations is correct. Use the graph of

f (x) = \log_{0.5} x

given below.

\log_{0.5} \frac{1}{3} > \log_{0.5} 1 > \log_{0.5} \frac{4}{3} > \log_{0.5} 2 > \log_{0.5} 5

\log_{0.5} 5 > \log_{0.5} 2 > \log_{0.5} \frac{4}{3} > \log_{0.5} 1 > \log_{0.5} \frac{1}{3}

\log_{0.5} 1 > \log_{0.5} \frac{1}{3} > \log_{0.5} \frac{4}{3} > \log_{0.5} 2 > \log_{0.5} 5

\log_{0.5} \frac{1}{3} > \log_{0.5} \frac{4}{3} > \log_{0.5} 1 > \log_{0.5} 2 > \log_{0.5} 5

1003136509

Level:

How many of the following inequalities is/are true?

\begin{aligned} \log_{7} 4 & > \log_{7} 11; & \log_{0.4} 0.7 & \leq \log_{0.4} 3 \\ \log_{\frac{1}{7}} 4 & \geq \log_{\frac{1}{7}} 0.4; & \log_{3} 0.11 & < \log_{3} 6 \end{aligned}

1

2

3

0

1003136508

Level:

What are the values of the real parameter

a

, that satisfy inequality

\log_{a} 7 < \log_{a} 4

0 < a < 1

a > 1

a < 1

a > 0

1003136507

Level:

What are the values of the real parameter

a

, that satisfy inequality

\log_{a} \frac{4}{7} > \log_{a} \frac{7}{4}

0 < a < 1

a > 1

a < 1

a > 0

1103136506

Level:

What are the values of the real variable

x

, if

\log_{4} x \leq \log_{4} 0.7

? Use the graph of

f (x) = \log_{4} x

given below.

x \in (0; 0.7]

x \in [0.7; \infty)

x \in [1; \infty)

x \in (- \infty; 0.7]

1103136505

Level:

What are the values of the real variable

x

, if

\log_{\frac{1}{4}} x > \log_{\frac{1}{4}} 3

? Use the graph of

f (x) = \log_{\frac{1}{4}} x

given below.

x \in (0; 3)

x \in (- \infty; 3)

x \in (3; \infty)

x \in (0; \infty)

1103136504

Level:

What are the values of the real variable

x

, if

\log_{7} x < 0

? Use the graph of

f (x) = \log_{7} x

given below.

x \in (0; 1)

x \in [1; \infty)

x \in (0; \infty)

x \in [0; 1]

1103138402

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