Question

Given the parent functions...?

Answer 1

\[f(x)=\log_2(3x-9)\] and \[g(x)=\log_2(x-3)\] what is \[f(x)-g(x)\]

Answer 2

@campbell_st

Answer 3

\[\log_2(2x-6)\]
\[\log_2(2x-12)\]
\[\log_2 \frac{ 1 }{ 3 }\]
\[\log_2 3\]

Answer 4

ok... so its simply

\[f(x) - g(x) = \log_{2} (3x - 9) - \log_{2}(x - 3)\]

ok... can you find a common factor in

\[(3x - 9)\]

Answer 5

Yes

Answer 6

what is it...?

Answer 7

x-3?

Answer 8

well you have

\[\log_{2}(3x - 9) = \log_{2}[3(x -3)] \]

do you know the log law for multiplication...?

Answer 9

No...

Answer 10

ok... this is what you need to use

\[\log(a \times b) = \log(a) + \log(b)\]

the law says that the log of a product is the same as the log of the sum of the factors

so your problem becomes

\[\log_{2}[3(x -3)] - \log_{2}(x -3) = \log_{2}(3) + \log_{2}(x -3) - \log_{2}(x -3)\]

now you should be able to simplify for the answer.

Answer 11

No solution exists...?

Answer 12

yes a solution does exist... can you see 2 terms that when you add them will result in a zero answer..?

Answer 13

Oh! I know what I did wrong. I tried to further simplify. But that can work. My answer is log_2 3

Answer 14

correct...