SOLUTION: Log(x+1)-log(x-1)=log 3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Log(x+1)-log(x-1)=log 3      Log On


   



Question 987697: Log(x+1)-log(x-1)=log 3
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing the problem for you, I will do one
that is solved EXACTLY in every detail to yours, so
that you can solve yours exactly the same way.  Every
step is the same in this problem as in yours: 

log%28%28x%2B3%29%29-log%28%282x-3%29%29%22%22=%22%22log%28%282%29%29

The difference of two logs is the log of the
quotient of what the logs are taken of.

So we write the left side as the log of a single
quantity:

log%28%28%28x%2B3%29%2F%282x-3%29%29%29%22%22=%22%22log%28%282%29%29

Since the logs of two quantities are equal, 
the two quantities are also equal.  So we can
drop the logs:

%28x%2B3%29%2F%282x-3%29%22%22=%22%222 

Multiply both sides by the LCD = (2x-3)

x%2B3%22%22=%22%222%282x-3%29

x%2B3%22%22=%22%224x-6

-3x%22%22=%22%22-9

x%22%22=%22%223

Edwin

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the rule:
+log%28a%29+-+log%28b%29+=+log%28+a%2Fb+%29+
-----------------------------
+log%28+x%2B1+%29+-+log%28+x-1+%29+=+log%28+3+%29+
+log+%28+%28+x%2B1+%29+%2F+%28+x-1+%29+%29+=+log+%283%29+
+%28+x%2B1+%29+%2F+%28+x-1+%29+=+3+
+x+%2B+1+=+3%2A%28+x-1+%29+
+x+%2B+1+=+3x+-+3+
+2x+=+4+
+x+=+2+
-------------
check:
+log%28+x%2B1+%29+-+log%28+x-1+%29+=+log%28+3+%29+
+log%28+2%2B1+%29+-+log%28+2-1+%29+=+log%28+3+%29+
+log%28+3+%29+-+log%28+1+%29+=+log%28+3+%29+
+log%28+3+%29+-+0+=+log%28+3+%29+
+3+=+3+
OK