Can someone tell me what I'm doing wrong here?

"Write the expression as a sum and/or difference of logarithms. Express powers as factors."

log3((x^9)/(x-6)) , x 6

And I answered "9log3x - 3log(x-6)" and it was incorrect. How do I fix it? (Rewriting to show clearer problem in comments.)

Question

Can someone tell me what I'm doing wrong here? 

"Write the expression as a sum and/or difference of logarithms. Express powers as factors."

log3((x^9)/(x-6)) , x > 6

And I answered "9log3x - 3log(x-6)" and it was incorrect. How do I fix it? (Rewriting to show clearer problem in comments.)

anonymous · Answer

$$\log _{3}(x ^{9}/(x-6)), x > 6$$  <-- Problem

$$9\log _{3}x - 3 \log (x-6)$$  <--- My incorrect answer.

shiraz14 · Answer

It should be 9log3(x) - log3(x-6). 
You mistreated the base as a power in your answer (only powers can be brought to the front of a log function, the base defines the log function and cannot be manipulated unless using a base-change).

anonymous · Answer

So to re-iterate, I just need to move my 3 to the other side of the 2nd log?

shiraz14 · Answer

The '3' is the base of the log in this case, i.e. to say, you are using log3 of a variable.

anonymous · Answer

I see now, thank you. :)

shiraz14 · Answer

To make it simpler to understand, consider the following:

3^x = y

If we wanted to find out what x is, we will use the following identity:
$$x = \log_{3}y$$

shiraz14 · Answer

You're welcome