## anonymous one year ago Given the parent functions f(x) = log2 (3x − 9) and g(x) = log2 (x − 3), what is f(x) − g(x)?

1. anonymous

@e.mccormick

2. mathstudent55

Subtract the functions.

3. mathstudent55

$$\Large f(x) = \log_2 (3x - 9)$$ $$\Large g(x) = \log_2 (x - 3)$$ $$\Large f(x) - g(x) = \log_2 (3x - 9) - \log_2 (x - 3)$$ Ok so far?

4. anonymous

yes @mathstudent55

5. mathstudent55

Now we need to simplify the fright side using some rules of logs. Here are two rules of logs: $$\Large \log ab = \log a + \log b$$ $$\Large \log \dfrac{a}{b} = \log a - \log b$$

6. anonymous

Alright.

7. anonymous

Ok, i thought we were going to factor lol

8. mathstudent55

Yes, we do factor. Look at the first log below compared to what it was. $$\Large f(x) - g(x) = \log_2 3(x - 3) - \log_2 (x - 3)$$

9. anonymous

you moved the 3 out of (3x-9) so u divide by 3

10. mathstudent55

I only factored out the 3. 3(x - 3) = 3x - 9. We are still taking the log of the same quantity, only it is now written in a different form, its factored form. Now we use the first rule of logs above to deal with the first log in our equation.

11. mathstudent55

I'm now working on the red part: $$\Large f(x) - g(x) = \color{red}{\log_2 3(x - 3)} - \log_2 (x - 3)$$ $$\Large f(x) - g(x) = \color{red}{\log_2 3 + \log_2 (x - 3)} - \log_2 (x - 3)$$ You see how the rule of logs is applied?

12. anonymous

Yes :)

13. mathstudent55

What can you do to the green part below? $$\Large f(x) - g(x) = \log_2 3 + \color{green}{\log(x - 3) - \log_2 (x - 3)}$$

14. anonymous

Cancel out?

15. anonymous

would the answer be log 2 1/3

16. mathstudent55

Correct.

17. mathstudent55

$$\Large f(x) - g(x) = \log_2 3$$

18. anonymous

is it log 2 3 or log 2 1/3?

19. mathstudent55

Answer is: $$\Large f(x) - g(x) = \log_2 3$$

20. anonymous

Alright, Thanksss! :)

21. mathstudent55

You're welcome.

22. anonymous

Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)? for this one, i got f(x) • g(x) = log10 x5x − 2

23. anonymous

Was I right?

24. mathstudent55

Here you need to multiply a log by a binomial. $$\Large f(x) = \log_{10} x$$ $$\Large g(x) = 5x − 2$$ Multiply the left sides together and multiply the right sides together: $$\Large f(x) \cdot g(x) = \log_{10} x \cdot (5x - 2)$$ Use the commutative property on the right side: $$\Large \color{red}{f(x) \cdot g(x) = (5x - 2)\log_{10} x}$$ Now use the distributive property: $$\Large \color{green}{f(x) \cdot g(x) = 5x\log_{10} x - 2 \log_{10} x}$$

25. mathstudent55

You were close. The idea was correct, but you need to use parentheses.

26. mathstudent55

Any of the lines above is a correct answer, but to make the line in black clearer, I think it's better to write it as: $$\Large f(x) \cdot g(x) = (\log_{10} x) (5x - 2)$$

27. anonymous

Okay! Thanks :)