SOLUTION: log(1-x)- Log(2+x)=2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log(1-x)- Log(2+x)=2      Log On


   

Question 1067887: log(1-x)- Log(2+x)=2
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28%28+1-x+%29%29+-+log%28%28+2%2Bx+%29%29+=+2+
I assume the base of the logs is +10+
Use the substitution +2+=+log%28+100+%29+
+log%28+%28%281-x%29%2F%282%2Bx%29%29+%29+=+log%28100%29+
+%28+1-x+%29%2F%28+2%2Bx+%29+=+100+
+1+-+x+=+100%2A%28+2%2Bx+%29+
+1+-+x+=+200+%2B+100x+
+101x+=+-199+
+x+=+-1.970297+
---------------------
check answer:
+log%28%28+1-x+%29%29+-+log%28%28+2%2Bx+%29%29+=+2+
+log%28%28+1-%28-1.970297+%29%29+-+log%28%28+2%2B1.970297+%29%29%29+=+2+
+log%28%28+2.970297+%29%29+-+log%28%28+.02970297+%29%29+=+log%28%28+100+%29%29+
+log%28%28+2.970297%2F.02970297+%29%29+=+log%28%28+100+%29%29+
+log%28%28+99.99999899+%29%29+=+log%28%28+100+%29%29+
OK
Get another opinion if needed

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
On logarithms and their properties see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".