SOLUTION: Hello everyone! I need help with logarithmic functions please! This is a hard topic for me and could use all the help I can. Find the domain of the logarithmic function.. f(

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello everyone! I need help with logarithmic functions please! This is a hard topic for me and could use all the help I can. Find the domain of the logarithmic function.. f(      Log On


   

Question 535345: Hello everyone! I need help with logarithmic functions please! This is a hard topic for me and could use all the help I can.

Find the domain of the logarithmic function..
f(x)= log(x^2-17x+72)
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain of the logarithmic function..
f(x)= log(x^2-17x+72)
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x^2-17x+72 must be > 0
(x-9)(x-8) > 0
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Draw a number line and plot x=8 and x=9
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Look for solutions in the intervals:
Try x = 0: -*- > 0 ; true, so solutions in (-oo,8)
Try x = 8.5: -*+ > 0 ; false
Try x = 9.5: +*+ > 0 ; true, so solutions in (9,+oo)
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Domain: (-oo,8)U(9,+oo)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=+log%28%28x%5E2-17x%2B72%29%29+
" logs are exponents " That's worth repeating.
It's important how you read this equation.
+x%5E2-17x%2B72+ is what I get when I
raise 10 to the exponent +f%28x%29+
-------------------------------
The thing to see here is that there is no way
you can end up with a negative by raising
10 to some power like +f%28x%29+
so, +x%5E2-17x%2B72+ can't be negative.
But, the log of this can be negative,
positive or zero
the domain is
- infinity < f(x) < + infinity