SOLUTION: find the domain of the function f(x)=log(base 10){1-log(base10)(x^2-5x+16)}

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Question 798863: find the domain of the function f(x)=log(base 10){1-log(base10)(x^2-5x+16)}
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=log%2810%2C%281-log%2810%2C%28x%5E2-5x%2B16%29%29%29%29
Logarithms are only defined for positive numbers, so f%28x%29 exists only when
1-log%2810%2C%28x%5E2-5x%2B16%29%29%3E0 and x%5E2-5x%2B16%3E0
Luckily, x%5E2-5x%2B16%3E0 for all real values of x.

1-log%2810%2C%28x%5E2-5x%2B16%29%29%3E0 <--> 1%3Elog%2810%2C%28x%5E2-5x%2B16%29%29 <--> 10%3Ex%5E2-5x%2B16 <--> 0%3Ex%5E2-5x%2B16-10 <--> 0%3Ex%5E2-5x%2B6 <--> 0%3E%28x-3%29%28x-2%29 <--> highlight%282%3Cx%3C3+%29