SOLUTION: log(x-6)- log (x-2) = log 5/x this is how I attempted to solve the problem (x-6) - (x-2) = log 5 - log x x-6-x+2 = 5 - x -6+2-5 = -y -9=-x 9=x I came up with x=9, but my a

Question 588203: log(x-6)- log (x-2) = log 5/x
this is how I attempted to solve the problem
(x-6) - (x-2) = log 5 - log x
x-6-x+2 = 5 - x
-6+2-5 = -y
-9=-x
9=x
I came up with x=9, but my answer key says the answer is 10. Will you please show me how to do this problem?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
log(x-6)- log (x-2) = log 5/x
log(x-6)- log (x-2) - log 5/x=0
log(x-6)- (log (x-2) + log 5/x)=0
place under single log
log[(x-6)/(x-2)*5/x]=0
convert to exponential form: base(10) raised to log of number(0)=number[(x-6)/(x-2)*5/x]
10^0=[(x-6)/(x-2)*5/x]=1
x-6=(x-2)*5/x=(5x-10)/x
x^2-6x=5x-10
x^2-11x+10=0
(x-10)(x-1)=0
x=1 (reject, (x-2)>0)
or
x=10

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