Lesson 3 Chopping Logs Solidify Understanding

Ready

Rewrite the following expressions with an exponent instead of a radical.

1.

$\sqrt[5]{x}$

2.

$\sqrt[7]{s^{2}}$

3.

$\sqrt[3]{w^{8}}$

4.

$\sqrt[3]{8 r^{6}}$

5.

$\sqrt[5]{125 m^{5}}$

6.

$\sqrt[3]{{(8 x)}^{2}}$

7.

$\sqrt[3]{9 b^{8}}$

8.

$\sqrt{75 x^{6}}$

Rewrite with a fractional exponent. Then evaluate.

9.

$\log_{3} \sqrt[5]{3} =$

10.

$\log_{2} \sqrt[3]{4} =$

11.

$\log_{7} \sqrt[5]{343} =$

12.

$\log_{5} \sqrt[5]{3,125} =$

Set

13.

Given $f (x) = \log_{3} \frac{x}{27}$

Use the graph to write an equivalent function for $f (x)$ .

14.

Given $g (x) = \log_{3} 3 x$

Use the graph to write an equivalent function for $g (x)$ .

15.

Given $h (x) = \log_{10} 40 x$ , select ALL of the functions that are equivalent. For each function that you select, show why it is equivalent to $h (x)$ .

$a (x) = \log_{10} x + \log_{10} 5 + \log_{10} 8$

$b (x) = \log_{10} x + \log_{10} 4 + 1$

$c (x) = \frac{\log_{10} 80 x}{\log_{10} 2}$

16.

Given $g (x) = \log_{5} 3 x + 2$ , select ALL of the functions that are equivalent. For each function that you selected, explain why it is equivalent to $g (x)$ .

$a (x) = \log_{5} 125 + \log_{5} 25 x$

$b (x) = \log_{5} 75 x$

$c (x) = \log_{5} 9 x - \log_{5} 3 + \log_{5} \sqrt{625} + \log_{5} 1$

$d (x) = \log_{5} 50 + \log_{5} 36 x - \log_{5} 4 - \log_{5} 3 - \log_{5} 2$

Go

Convert to logarithmic form.

17.

$2^{9} = 512$

18.

$10^{- 2} = 0.01$

19.

${(\frac{2}{3})}^{- 1} = \frac{3}{2}$

Write in exponential form.

20.

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

21.

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

22.

$\log_{\frac{2}{5}} \frac{8}{125} = 3$