SOLUTION: log3(x-1)+log3(x-7)=3

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Question 308664: log3(x-1)+log3(x-7)=3
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
By the law of logarithms,
log%283%2C%28x-1%29%29%2Blog%283%2C%28x-7%29%29+=3 becomes log%283%2C%28x-1%29%28x-7%29%29=3

By the definition of logarithms, this becomes
3%5E3=%28x-1%29%28x-7%29+
27=x%5E2-8x%2B7
0=x%5E2-8x-20
0=%28x-10%29%28x%2B2%29

There appear to be two solutions: x=10 and x=-2.

However, you cannot have a log of a negative number, so x=-2 must be rejected. The solution is x=10.

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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus