SOLUTION: Please help! Thanks tutors! log2(x-1)

SOLUTION: Please help! Thanks tutors! log2(x-1) - log2(x+3)= log2(1/x)

Question 110200: Please help! Thanks tutors!
log2(x-1) - log2(x+3)= log2(1/x)
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To solve for x, first recognize that the difference of the logs (to the same base) of two quantities
is equal to the log of the division of the two quantities.
.
Using this rule of logarithms means you can convert:
.
to
.
Substitute this conversion into the equation and it becomes:
.

.
Look carefully at this. For the left side to be equal to the right side, the two quantities undergoing
the log operator must be equal. That means:
.

.
This is a proportion and you can simplify proportions by cross multiplying ... multiplying
the numerator by the denominator on the other side ... for both numerators.
.
When you do that you get:
.

.
Multiply out both sides and this equation becomes:
.

.
Get rid of the x on the right side by subtracting x from both sides to get:
.

.
Then get rid of the 3 on the right side by subtracting 3 from both sides to get:
.

.
The left side of this equation factors to:
.

.
This equation will be true if either of the factors is zero ... which would cause a
multiplication by zero on the left side and therefore make the left side become zero which equals
the right side. Note that one of the factors will be zero if x = +3 or if x = -1.
.
Note however that if x equals -1, several of the terms on which the log function is operating
will become negative, and the log of a negative number is not permitted. Therefore,
x = +3 is the only valid answer.
.
Hope this helps you to understand the problem and the steps you can go through to solve
for x.
.
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