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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)?
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)?

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Subtract the functions.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large f(x) = \log_2 (3x  9)\) \(\Large g(x) = \log_2 (x  3)\) \(\Large f(x)  g(x) = \log_2 (3x  9)  \log_2 (x  3)\) Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to simplify the fright side using some rules of logs. Here are two rules of logs: \(\Large \log ab = \log a + \log b\) \(\Large \log \dfrac{a}{b} = \log a  \log b\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, i thought we were going to factor lol

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, we do factor. Look at the first log below compared to what it was. \(\Large f(x)  g(x) = \log_2 3(x  3)  \log_2 (x  3)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you moved the 3 out of (3x9) so u divide by 3

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1I 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.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1I'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?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1What can you do to the green part below? \(\Large f(x)  g(x) = \log_2 3 + \color{green}{\log(x  3)  \log_2 (x  3)}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the answer be log 2 1/3

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large f(x)  g(x) = \log_2 3 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it log 2 3 or log 2 1/3?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Answer is: \(\Large f(x)  g(x) = \log_2 3 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, Thanksss! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Given 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

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here 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: \(\Large \color{green}{f(x) \cdot g(x) = 5x\log_{10} x  2 \log_{10} x}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You were close. The idea was correct, but you need to use parentheses.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Any 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: \(\Large f(x) \cdot g(x) = (\log_{10} x) (5x  2)\)
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