Lesson 4 Log-Arithm-etic Practice Understanding

Ready

1.

Factor out the greatest common factor in the expression. Then simplify the numbers inside the parentheses.

Factor out the GCF	Factored Form	Simplified Expression
$7 + 7 (0.675)$
$19 + 19 (0.33)$
$38 - 38 (0.42)$
$67 - 67 (0.92)$

2.

Jaxon has invested $$ 500$ in an excellent money market account that earns $20 %$ per year. Given is a chart of his year-end balances that appeared on his investment statements.

Beginning Balance	End of year $1$	End of year $2$	End of year $3$
$$ 500$	$$ 600$	$$ 720$	$$ 864$

Jaxon’s money is growing exponentially, and he recalls from a previous math class that the formula for an exponential function is $y = a b^{x}$ . He recalls that $a = $ 500$ and $x = # years$ . He thinks $b$ should equal $20 %$ $(0.2)$ , but that number isn’t giving him the numbers on his bank statement. What number should he be using for $b$ ? Explain.

3.

Jackie owes $$ 500$ on a loan. She has agreed to pay the loan company $8 %$ of the outstanding balance on the first day of each month. Given is a chart of the balances she owes after each payment.

Initial Amount Owed	Month 1	Month 2	Month 3
$$ 500$	$$ 460$	$$ 423.20$	$$ 389.34$

Jackie knows her loan balance is decreasing exponentially. She also recalls from a previous math class that the formula for an exponential function is $y = a b^{x}$ . She replaces $a$ with $$ 500$ and lets $x$ be the number of monthly payments. But when she uses $8 %$ $(0.08)$ in the formula for $b$ , it doesn’t give her the correct balance for each month. What number should she be using for $b$ ? Explain.

Set

Use properties of logarithms to rewrite the indicated logarithms in terms of the given values, then find the indicated logarithm using the given approximate values.

Do not use a calculator to evaluate the logarithms.

Given:

$\begin{array}{l} \log 16 \approx 1.2 \\ \log 5 \approx 0.7 \\ \log 8 \approx 0.9 \end{array}$

4.

Find $\log \frac{5}{8}$

5.

Find $\log 25$

6.

Find $\log \frac{1}{2}$

7.

Find $\log 80$

8.

Find $\log \frac{1}{64}$

Given:

$\begin{array}{l} \log_{3} 2 \approx 0.6 \\ \log_{3} 5 \approx 1.5 \end{array}$

9.

Find $\log_{3} 16$

10.

Find $\log_{3} 108$

11.

Find $\log_{3} \frac{3}{50}$

12.

Find $\log_{3} \frac{8}{15}$

13.

Find $\log_{3} 486$

14.

Find $\log_{3} 18$

15.

Find $\log_{3} 120$

16.

Find $\log_{3} \frac{32}{45}$

Go

Use your calculator and the definition of $\log x$ to find the value of $x$ . (Round your answers to four decimals.)

17.

$\log x = - 3$

18.

$\log x = 1$

19.

$\log x = 0$

20.

$\log x = \frac{1}{2}$

21.

$\log x = 1.75$

22.

$\log x = - 2.2$

23.

$\log x = 3.67$

24.

$\log x = \frac{3}{4}$

25.

$\log x = 6$