Calculations with logarithms | math4u.vsb.cz

2000014106

Level:

B

Find the value of

\log_{2} 5 + \log_{2} 20

if

\log_{2} 5 = a

and

\log_{2} 20 = b

.

2 a + 2

2^{a} + 2^{b}

a b

5 a

2000014105

Level:

C

Find the value of

(\log_{\frac{1}{a}} b) \cdot (\log_{\frac{1}{b}} c) \cdot (\log_{\frac{1}{c}} a)

.

- 1

\frac{1}{a b c}

a b c

1

2000014104

Level:

C

Find the value of

L

if

L = \log_{\sqrt{2}} 2 \cdot \log_{2} \sqrt{3} \cdot \log_{\sqrt{3}} 4

.

L = 4

L = 2

L = 3

L = 1

2000014103

Level:

C

Find the value of

\log_{a b} x

if

\log_{a} x = 2

and

\log_{b} x = 3

.

\frac{6}{5}

\frac{1}{6}

6

\frac{5}{6}

2010011005

Level:

B

If

a

,

b

,

c \in (0; \infty)

then the expression

\log_{2} a + 3 \log_{2} b - \frac{1}{2} \log_{2} c

is equivalent to:

\log_{2} \frac{a b^{3}}{\sqrt{c}}

\log_{2} \frac{3 a b}{\frac{1}{2} c}

\log_{2} (a b^{3} c^{\frac{1}{2}})

\log_{2} (- \frac{3}{2} a b c)

2010011004

Level:

C

If

x \in (0; 1) \cup (1; \infty)

then the product

(\log_{x} 4) (\log_{16} x)

can be written as:

\frac{1}{2}

2

\log_{x} 4 + \log_{16} x

\frac{1}{4}

2010011003

Level:

A

Find the value of

x

, if

\log_{\frac{1}{3}} x = - 4

.

x = 81

x = \frac{1}{81}

x = - 81

x = \frac{1}{12}

2010011002

Level:

A

Which of the following statements is not true?

\log_{\frac{1}{2}} 6 = - 3

\log_{\frac{1}{2}} 8 = - 3

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

\log_{\frac{1}{2}} \frac{1}{4} = 2

2010011001

Level:

A

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

\sqrt{16} = 4

\log_{16} 4 = \frac{1}{2}

\log_{\frac{1}{2}} 16 = 4

\log_{4} \frac{1}{2} = 16

\log_{2} 4 = 16

2000000606

Level:

A

The value of the expression

3 \log_{4} 2 - \frac{1}{2} \log_{4} 16

is:

0.5

2

\log_{4} \frac{9}{256}

\frac{3}{2} \log_{4} \frac{1}{8}