SOLUTION: log (x-4) - log (x+5) = 1

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Question 636455: log (x-4) - log (x+5) = 1
Found 2 solutions by lwsshak3, DrBeeee:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
log (x-4) - log (x+5) = 1
place under single log
log[(x-4)/(x+5)]=1
convert to exponential form
10^1=(x-4)/(x+5)=10
10x+50=x-4
9x=-54
x=-6
no solution, (x-4) and (x+5)>0

Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website!
Using the identity Log(a/b) = Log a - Log b
and Log(10) = 1
We have
(1) Log[(x-4)/(x+5)] = Log(10)
Which equates to
(2) (x-4)/(x+5) = 10
Simplify (2) to obtain
x-4 = 10x + 50
-9x = 54
x = -6
Is this correct?
Substitute x = -6 into (1)
Does {Log[(-6-4)/(-6+5)] = 1}?
Does {Log[(-10)/(-1)] = 1}?
Does {Log[10] = 1}?
Does [1 = 1}? Yes
The solution is x = -6.