Free Printable Math 3 LT #1 Review

1.

Write the following in logarithmic form:

$2^3=8$

a)

$\log_23\ =\ 8$

b)

$\log_28\ =\ 3$

c)

$\log_32\ =\ 8$

2.

Write the following in logarithmic form:

x\ ^y\ =\ z

a)

$\log_x\ y\ =\ z$

b)

$\log_{x\ }z\ =\ y$

c)

$\log_{y\ }x\ =\ z$

3.

Evaluate:

\log_{5\ }625\ =\

a)

5

b)

4

c)

3

d)

2

4.

Evaluate:

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

a)

-2

b)

-1

c)

0

d)

2

5.

Evaluate:

\log_{\frac{1}{3}\ }3\ =\

a)

-2

b)

-1

c)

0

d)

2

6.

Use the properties of logarithms to expand and simplify each logarithmic expression:

\log_33x

a)

$\log_33\ +\ \log_3x$

b)

$\log_33\cdot\log_3x$

c)

$1+\log_3x$

d)

$\log_33-\log_3x$

7.

Use the properties of logarithms to expand and simplify each logarithmic expression:

\log_327x

a)

$\log_327\ +\ \log_3x$

b)

$\log_327\cdot\log_3x$

c)

$3+\log_3x$

d)

$\log_327-\log_3x$

8.

Use the properties of logarithms to expand each logarithmic expression:

\log_ax^4y^5z^3

a)

$4\log_ax\ \cdot\ 5\log_ay\cdot3\log_az$

b)

$\log_ax^4\ +\ \log_ay^5+\log_az^3$

c)

$4\log_ax\ -\ 5\log_ay-3\log_az$

d)

$4\log_ax\ +\ 5\log_ay+3\log_az$

9.

Use the properties of logarithms to condense the logarithmic expression: $\ 3\left(\log_x\ y\ -\log_xz\right)\$

a)

$\ 3\log_x\ y\ -3\log_xz\$

b)

$\ 3\log_x\ y\cdot z\$

c)

$\ 3\log_x\ \frac{y}{z}\$

d)

$\ \log_x\left(\ \frac{y}{z}\ \right)^3$

10.

Use the properties of logarithms to condense the logarithmic expression: $\ \frac{1}{2}\left(\log_x\ y\ +\log_xz\right)\$

a)

$\ \frac{1}{2}\log_x\ y\ +\frac{1}{2}\log_xz\$

b)

$\ \frac{1}{2}\log_x\ y\cdot z\$

c)

$\ \log_x\ \sqrt{yz}\$

d)

$\ \log_x\sqrt{\frac{y}{z}}$

11.

Use the properties of logarithms to condense each logarithmic expression:

\log_3x\ +\frac{1}{2}\log_3y-\log_3z

a)

$\log_3x\ \cdot\frac{1}{2}\log_3y\div\log_3z$

b)

$\log_3\ \frac{x\sqrt{y}}{z}$

c)

$\log_{3\ }x\ +\frac{1}{2}y-z$

d)

$\log_3\ x\sqrt{y}z$

12.

Use the given values and the properties of logarithms to find the indicated logarithm.
Given: $\log_23\ \approx\ 0.8,\ \log_25\ \approx\ 1.2\ and\ \log_27\ \approx\ 1.4$

Find:

\log_245\ \approx

a)

2.0

b)

14

c)

2.8

d)

0.79

13.

Use the given values and the properties of logarithms to find the indicated logarithm.
Given: $\log_23\ \approx\ 0.8,\ \log_25\ \approx\ 1.2\ and\ \log_27\ \approx\ 1.4$

Find:

\log_242\ \approx

a)

2.2

b)

14

c)

2.8

d)

3.2

Math 3 LT #1 Review

Total questions: 13

Worksheet time: 15mins

Similar Resources on Wayground