Lesson 2 Falling Off a Log Solidify Understanding

Ready

Evaluate each logarithm.

1.

$\log_{5} 625 =$

2.

$\log_{3} 243 =$

3.

$\log_{5} 0.2 =$

4.

$\log_{9} 81 =$

5.

$\log 1,000,000 =$

6.

$\log_{x} x^{7} =$

Set

7.

The graph of $f (x) = \log_{3} x$ is shown. Which point on the graph tells you the base of the logarithm?

8.

The graph of $g (x) = \log_{5} x$ is shown. Which point on the graph tells you the base of the logarithm?

9.

Explain why the graphs of both logarithmic functions with different bases contain the point $(1, 0)$ .

10.

The graph shows a logarithmic function that has been transformed. Write the function for this graph.

11.

The graph shows a logarithmic function that has been transformed. Write the function for this graph.

12.

The graph shows a logarithmic function that has been translated vertically and horizontally. Write the function for this graph.

(The dotted lines are the transformed axes that could help you write the equation.)

13.

The graph shows a logarithmic function that has been translated vertically and horizontally. Write the function for this graph.

(The dotted lines are the transformed axes that could help you write the equation.)

Go

Rewrite each expression. Answers should have only positive exponents.

14.

${(2^{3})}^{4}$

15.

${(x^{3})}^{2}$

16.

${(a^{3})}^{- 2}$

17.

${(2^{3} w)}^{4}$

18.

${(b^{- 7})}^{3}$

19.

${(d^{- 3})}^{- 2}$

20.

$x^{2} \cdot {(x^{5})}^{2}$

21.

$m^{- 3} \cdot {(m^{2})}^{3}$

22.

${(x^{5})}^{- 4} \cdot x^{25}$

23.

${(5 a^{3})}^{2}$

24.

${(6^{- 3})}^{2}$

25.

${(2 a^{3} b^{2})}^{2}$