log(x) + log (x-3) = 1
When you take a log out of two terms, an addition becomes
a multiplication and a subtraction becomes a division:
log[(x)(x-3)] = 1
Now take the antilog of both sides, remembering that the
antilog of 1 is 10.
(x)(x-3) = 10
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0
Set the first factor = 0
x - 5 = 0.
x = 5
That checks:
log(x) + log(x-3)= 1
log(5) + log(5-3) = 1
log(5) + log(2) = 1
.6989700043 + .301010299957 = 1
1 = 1
Set the secod factor = 0
x + 2 = 0
x = -2
We must discard that, because when
we try to check it:
log(-2) + log(-2-3) = 1
log(-2) + log(-5) = 1
Logs can only be taken of positive
numbers, so the left side is not defined.
There is but one solution, x = 5
That involves log(0) which is not
defined.
Edwin
