Asked by Anonymous
Log(x-6) +Log(x+3)=1
Solve for x
I think it has no solution but why?
Solve for x
I think it has no solution but why?
Answers
Answered by
Steve
well, work it out...
log(x-6)+log(x+3) = 1
log (x-6)*(x-3) = 1
(x-6)*(x-3) = 10
x^2-9x+18 = 10
x^2-9x+8 = 0
(x-1)(x-8) = 0
x = 1 or 8
x=1 does not work, because then x-6 < 0 and the log is not defined. So, the only real solution is x=8
Check:
log(2)+log(5) = 1
log(10) = 1
yes.
log(x-6)+log(x+3) = 1
log (x-6)*(x-3) = 1
(x-6)*(x-3) = 10
x^2-9x+18 = 10
x^2-9x+8 = 0
(x-1)(x-8) = 0
x = 1 or 8
x=1 does not work, because then x-6 < 0 and the log is not defined. So, the only real solution is x=8
Check:
log(2)+log(5) = 1
log(10) = 1
yes.
Answered by
Steve
Hmmm. Let's try that again without the typo...
log (x-6)*(x+3) = 1
x^2-3x-18 = 10
x^2-3x-28 = 0
x = (3±11)/2
x = -4 or 7
The only real solution is x=7
Check:
log(1)+log(10) = 1
yes
log (x-6)*(x+3) = 1
x^2-3x-18 = 10
x^2-3x-28 = 0
x = (3±11)/2
x = -4 or 7
The only real solution is x=7
Check:
log(1)+log(10) = 1
yes
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