SOLUTION: find the domain of f(x)=log(x-5) squared

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Question 818644:
find the domain of f(x)=log(x-5) squared
Found 2 solutions by jsmallt9, LinnW:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The answer depend on what is being squared. Is it
f%28x%29=%28log%28%28x-5%29%29%29%5E2
or
f%28x%29=log%28%28%28x-5%29%5E2%29%29?
Since I don't know which is right I cannot solve the problem. But I can tell you what to do. The arguments of all logarithms must be positive. So the solution will be whatever x-values will make the argument positive. So:
  • If the first equation is correct, then argument is x-5. The domain will be the solution to:
    x - 5 > 0
  • If the second equation is correct, then the argument is %28x-5%29%5E2.. The domain will be the solution to:
    %28x-5%29%5E2+%3E+0
    Note: Since squaring something never results in a negative, the only x's that are not in the domain are the x's that make %28x-5%29%5E2 zero. So an alternate way to find the domain is to solve:
    %28x-5%29%5E2+=+0
    and then the domain is all real numbers except the solution(s) to the equation above.

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
If you mean f%28x%29=log%28%28%28x-5%29%5E2%29%29
then the domain is all real numbers since
%28%28x-5%29%5E2%29 will always result in a positive number.