Asked by Anonymous

Log(x-6) +Log(x+3)=1
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.
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

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