Calculations with logarithms | math4u.vsb.cz

1003102413

Level:

B

Let

x

,

y

,

z \in (0; \infty)

. Find the equivalent form of the following expression.

\log \sqrt{\frac{x z^{2}}{y^{16}}}

\frac{1}{2} \log x - 8 \log y + \log z

\frac{1}{2} \log x + 8 \log y - \log z

8 \log x + \frac{1}{2} \log y - \log z

\log x - 16 \log y + 2 \log z

1003102414

Level:

B

From the given expressions choose the one equivalent to

\log (8 \cdot \sqrt[3]{75})

, if

\log 2 = a

,

\log 3 = b

and

\log 5 = c

.

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

3 a + \frac{1}{3} b + \frac{1}{3} c

4 a + \frac{1}{3} b + \frac{2}{3} c

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

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

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)

2010016001

Level:

B

The value of the expression

\log 25^{4} + \log 4^{4}

is:

8

4

4 + \log 29

8 + \log 29

2010016002

Level:

B

The value of the expression

\log 125^{2} + \log 8^{2}

is:

6

5

4 + \log 133

8 + \log 133

2010016003

Level:

B

The number

1 + \log_{2} 7

equals:

\log_{2} 14

3

4.5

\log_{2} 9

2010016004

Level:

B

The number

\log_{3} 6 - 1

equals:

\log_{3} 2

\log_{3} 5

5

1

1003102407

Level:

C

If

\log_{a} b = 100

and

\log_{4} a = 10

then the value of

b

is:

2^{2000}

2^{1000}

2^{1002}

2^{200}

1003102410

Level:

C

If

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

then the product

(\log_{x} 3) (\log_{5} x)

can be written as:

\log_{5} 3

\log_{3} 5

\log_{5 x} (3 x)

\log_{x} 3 + \log_{5} x