SOLUTION: how do you solve the following logarithmic equation {{{log^3(x-2)+log^3(x-8)=3}}} be sure to reject the domain and expressions

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Question 544494: how do you solve the following logarithmic equation log%5E3%28x-2%29%2Blog%5E3%28x-8%29=3 be sure to reject the domain and expressions
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
log^3(x-2)+log^3(x-8)=3
log3[(x-2)(x-8)]=3
convert to exponential form: base(3) raised to log of number(3)=number[(x-2)(x-8)]
3^2=[(x-2)(x-8)]=9
x^2-10x+16=0
(x-8)(x-2)=0
x=8 (reject, (x-8)>0)
or
x=2 (reject, (x-8)>0)
Therefore, no solution