Given the parent functions f(x) = log2 (3x − 9) and g(x) = log2 (x − 3), what is f(x) − g(x)?

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Given the parent functions f(x) = log2 (3x − 9) and g(x) = log2 (x − 3), what is f(x) − g(x)?

Mathematics
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@e.mccormick
Subtract the functions.
\(\Large f(x) = \log_2 (3x - 9)\) \(\Large g(x) = \log_2 (x - 3)\) \(\Large f(x) - g(x) = \log_2 (3x - 9) - \log_2 (x - 3)\) Ok so far?

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Other answers:

Now we need to simplify the fright side using some rules of logs. Here are two rules of logs: \(\Large \log ab = \log a + \log b\) \(\Large \log \dfrac{a}{b} = \log a - \log b\)
Alright.
Ok, i thought we were going to factor lol
Yes, we do factor. Look at the first log below compared to what it was. \(\Large f(x) - g(x) = \log_2 3(x - 3) - \log_2 (x - 3)\)
you moved the 3 out of (3x-9) so u divide by 3
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.
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?
Yes :)
What can you do to the green part below? \(\Large f(x) - g(x) = \log_2 3 + \color{green}{\log(x - 3) - \log_2 (x - 3)}\)
Cancel out?
would the answer be log 2 1/3
Correct.
\(\Large f(x) - g(x) = \log_2 3 \)
is it log 2 3 or log 2 1/3?
Answer is: \(\Large f(x) - g(x) = \log_2 3 \)
Alright, Thanksss! :)
You're welcome.
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
Was I right?
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: \(\Large \color{green}{f(x) \cdot g(x) = 5x\log_{10} x - 2 \log_{10} x}\)
You were close. The idea was correct, but you need to use parentheses.
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: \(\Large f(x) \cdot g(x) = (\log_{10} x) (5x - 2)\)
Okay! Thanks :)

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