SOLUTION: HElp! could you please do this (I couldn't) Simplify: 9log(base 27)x - 4log(base 9)x The answer is log(base3)x but I don't know how to get that! Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: HElp! could you please do this (I couldn't) Simplify: 9log(base 27)x - 4log(base 9)x The answer is log(base3)x but I don't know how to get that! Thank you.      Log On


   

Question 260352: HElp! could you please do this (I couldn't)
Simplify: 9log(base 27)x - 4log(base 9)x
The answer is log(base3)x but I don't know how to get that! Thank you.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem
(i) 9log%2827%2Cx%29+-+4log%289%2Cx%29+
Here are the step I took:
step 1 - write 9log%2827%2Cx%29+=+Y and solve for Y
27%5EY+=+x%5E9
%283%5E3y%29+=+x%5E9
taking a log base 3 of both sides, we get
3y+=+log%283%2Cx%5E9%29
y+=+%289%2F3%29log%283%2Cx%29+=+3log%283%2Cx%29
--
step 2 - write 4log%289%2Cx%29+=+Z and solve for Z
9%5EZ+=+x%5E4
%283%5E2Z%29+=+x%5E4
taking a log base 3 of both sides, we get
2Z+=+log%283%2Cx%5E4%29
y+=+%284%2F2%29log%283%2Cx%29+=+2log%283%2Cx%29
--
step 3 - rewriting steps 1 and 2, we get
3log%283%2Cx%29+-+2log%283%2Cx%29
which is simply
log%283%2Cx%29