SOLUTION: Hello. I am on my last homework problem and am having a horrible hard time with this problem. Any help would be so appreciated. Thank you ln(x+3)-ln(x-6)=4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello. I am on my last homework problem and am having a horrible hard time with this problem. Any help would be so appreciated. Thank you ln(x+3)-ln(x-6)=4      Log On


   

Question 814378: Hello. I am on my last homework problem and am having a horrible hard time with this problem. Any help would be so appreciated. Thank you
ln(x+3)-ln(x-6)=4
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+ln%28x%2B3%29+-+ln%28x-6%29+=+4+
The trick to solving this is
to make the substitution:
+4+=+ln%28+e%5E4+%29+
+ln%28+x%2B3+%29+-+ln%28+x-6+%29+=+ln%28+e%5E4+%29+
+ln%28+%28+x+%2B+3+%29+%2F+%28+x-+6+%29+%29+=+ln%28+e%5E4+%29+
+%28+x+%2B+3+%29+%2F+%28+x-+6+%29+=++e%5E4+
+x+%2B+3++=+e%5E4%2Ax+-+6%2Ae%5E4+
+e%5E4%2Ax+-+x+=+6%2Ae%5E4+%2B+3+
+x%2A%28+e%5E4+-+1+%29+=+6%2Ae%5E4+%2B+3+
+x+=+%28+6%2Ae%5E4+%2B+3+%29+%2F+%28+e%5E4+-+1+%29+
Hope I got it
The method should be OK