Lesson 5 Common Sense Solidify Understanding

Ready

The graphs of $f (x) = 10^{x}$ and $g (x) = \log x$ are shown in the same coordinate plane.

Make a list of the characteristics of each function.

1.

$f (x) = 10^{x}$

2.

$g (x) = \log x$

Each question below refers to the graphs of the functions $f (x) = 10^{x}$ and $g (x) = \log x$ . State whether they are true or false. If they are false, correct the statement so that it is true.

3.

Every graph of the function $g (x) = \log x$ will contain the point $(1, 0)$ .

True

False

4.

Both graphs have vertical asymptotes.

True

False

5.

The graphs of $f (x)$ and $g (x)$ have the same rate of change.

True

False

6.

The functions are inverses of each other.

True

False

7.

The range of $f (x)$ is the domain of $g (x)$ .

True

False

8.

The graph of $g (x)$ will never reach $3$ .

True

False

Set

Solve each equation. Write each answer as a logarithm and a decimal approximation.

9.

$10^{x} = 0.1$

10.

$10^{x - 3} = 202$

11.

$10^{x + 5} - 53 = - 124$

12.

$\frac{10^{2 x - 1}}{3} = 75$

13.

$4 (10^{x - 2}) + 3 = 2,021$

14.

$10^{5 x} = 10^{2 x - 7}$

Solve the following systems of equations.

15.

${\begin{cases} y = 10^{x} \\ y = 0.001 \end{cases}$

16.

${\begin{cases} y = 10^{x} - 5 \\ y = - \frac{1}{2} x - 4 \end{cases}$

17.

${\begin{cases} y = 10^{x} - 3 \\ y = - 3 x + 10 \end{cases}$

Go

Use long division to divide the following problems.

Write your answers as a quotient and a remainder. (Show each step.)

18.

$9 \overset{―}{) 2,179}$

19.

$12 \overset{―}{) 382}$

20.

$24 \overset{―}{) 461}$

21.

$13 \overset{―}{) 4,297}$

22.

$11 \overset{―}{) 1,579}$

23.

$62 \overset{―}{) 9,885}$