SOLUTION: log3(2x-3)-log3(x+2)=3 PLEASE HELP!

Question 1004909: log3(2x-3)-log3(x+2)=3
PLEASE HELP!
Found 2 solutions by fractalier, KMST:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Using the laws of exponents
log3(2x-3)-log3(x+2)=3
becomes
log(3) ((2x-3)/(x+2)) = 3
Now exponentiate 3-to-the and get
(2x-3)/(x+2) = 27
Now multiply by x+2 and solve
2x - 3 = 27x + 54
-57 = 25x
x = -57/25
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Logarithm of a quotient is the difference of the logarithms, so
--->
Logarithm of something is the exponent you have to apply the base to get that something, so if there is a solution,
--->---> .
The rest is simple algebra:
--->--->--->--->--->--->
The problem is that with , ,
and logarithm of a negative number is undefined.
So, there are .
We could have started with "there are no solutions with
<---><---> ".
For both logarithms exist, and .
Then, if you were in calculus class (and even if you weren't),
you would realize that in the domain of that function
increases with , and
increases with , so
increases with , and
,
so .
Graphing and we get

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