SOLUTION: Hello. Could you helpe solve this. Find the domain of the function s(x) = log7 (X^2 + 7X + 10). A little explanation will be appreciated. Thanks.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello. Could you helpe solve this. Find the domain of the function s(x) = log7 (X^2 + 7X + 10). A little explanation will be appreciated. Thanks.      Log On


   

Question 46193: Hello. Could you helpe solve this.
Find the domain of the function
s(x) = log7 (X^2 + 7X + 10). A little explanation will be appreciated. Thanks.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
s(x) = log%287%2Cx%5E2%2B7x%2B10%29
s(x) = log%287%2C%28x+%2B+5%29%28x+%2B+2%29%29
You can not take a logarithm of a negative number nor zero:
x+%2B+5+%3E+0
x+%3E+-5 check: log%287%2C%28x+%2B+5%29%28x+%2B+2%29%29 = log%287%2C%28-4+%2B+5%29%28-4+%2B+2%29%29 = log%287%2C%281%29%28-2%29%29 Nope
x+%2B+5+%3C+0
x+%3C+5 check: log%287%2C%28x+%2B+5%29%28x+%2B+2%29%29 = log%287%2C%28-6+%2B+5%29%28-6+%2B+2%29%29 = log%287%2C%28-1%29%28-4%29%29 = log%287%2C%284%29%29 Correct
and
x+%2B+2+%3E+0
x+%3E+-2 check: log%287%2C%28x+%2B+5%29%28x+%2B+2%29%29 = log%287%2C%281+%2B+5%29%281+%2B+2%29%29 = log%287%2C%286%29%283%29%29 = log%287%2C18%29 Correct
Domain: x < -5 and -2 < x
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Clog%287%2Cx%5E2%2B7x%2B10%29%29