SOLUTION: Hello! I was wondering if anybody could help me solve this equation. I really don't quite understand it. I looked into my algebra 2 book online and I still didn't really grasp the

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello! I was wondering if anybody could help me solve this equation. I really don't quite understand it. I looked into my algebra 2 book online and I still didn't really grasp the      Log On


   



Question 884647: Hello!
I was wondering if anybody could help me solve this equation. I really don't quite understand it. I looked into my algebra 2 book online and I still didn't really grasp the concept, so can someone please help me. Thank you in advance.
The equation is 1n(x+6)-1n(x)=!n(4). Give an exact solution.

Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28%28x%2B6%29%2F4x%29+=+0
e%5E0+=+1
%28%28x%2B6%29%2F4x%29+=+1
x + 6 = 4x
6 = 3x, x = 2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general rule to follow is:
+ln%28a%29+-+ln%28b%29+=+ln%28+a%2Fb+%29+
------------------------
To attempt to show why this is so,
suppose
+a+=+e%2Ae%2Ae%2Ae%2Ae%2Ae+ ( e = 2.2718 ), or
+a+=+e%5E5+
--------------
Also, suppose
+b+=+e%2Ae%2Ae%2Ae+, or
+b+=+e%5E4+
--------------
So, now I can say:
+ln%28a%29+-+ln%28b%29+=+ln%28e%5E5%29+-+ln%28e%5E4%29+
-----------------------------
+ln%28e%5E5%29+-+ln%28e%5E4%29+=+5+-+4+
+ln%28e%5E5%29+-+ln%28e%5E4%29+=+1+
-----------------------
If you don't understand this last line, then
you don't really know what a log is ( natural or not )
and you need intensive review
----------------------------
Now, to prove my definition:
+ln%28+a%2Fb+%29+=+ln%28+e%5E5+%2F+e%5E4+%29+
+ln%28+a%2Fb+%29+=+ln%28+e%5E1+%29+
+ln%28+a%2Fb+%29+=+1+
------------------
The definition works no matter what you
plug in for +a+ or +b+. I just made it easy.
-------------------
Now looking at your problem:
+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+
+ln%28+%28x%2B6%29%2Fx+%29+=+ln%28+4+%29+
------------------------
Is it clear that
+%28+x%2B6+%29%2Fx+=+4+ ?
--------------------
The basic definition would be:
If +ln%28a%29+=+ln%28b%29+, then
+a+=+b+
-----------------
+%28+x%2B6+%29%2Fx+=+4+
+x+%2B+6+=+4x+
+3x+=+6+
+x+=+2+
----------
Check:
+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+
+ln%28+2%2B6+%29+-+ln%28+2+%29+=+ln%284%29+
+ln%28+8+%29+-+ln%28+2+%29+=+ln%28+4+%29+
+ln%28+8%2F2+%29+=+ln%28+4+%29+
+ln%28+4+%29+=+ln%28+4+%29+
OK
Hope this helps