SOLUTION: 10. Solve the following logarithm equation. Please show all of your work. log(3x) = log4 + log(x – 1) please help!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 10. Solve the following logarithm equation. Please show all of your work. log(3x) = log4 + log(x – 1) please help!      Log On


   

Question 469364: 10. Solve the following logarithm equation. Please show all of your work.
log(3x) = log4 + log(x – 1)
please help!
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Use following log property
log+x+%2B+log+y+=+log+xy
Therefore
log+3x+=+log+4%28x-1%29
Since its the same log, you can conclude that it is equivalent to the equation:
3x+=+4%28x-1%29
**Note: Suppose you prove a = b, then log a = log b is proven as well **
Now distribute right side
3x+=+4x+-+4
Subtract 4x on both sides
-x+=+-4
Flip the signs
x+=+4
Verify by substituting 4 in for x
log+%283%29%284%29+=+log+%284%29%284-1%29
log+12+=+log+12
True statement, therefore solution x = 4 is correct