SOLUTION: log x + log (x - 3) = 2log2

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Question 78212: log x + log (x - 3) = 2log2
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
log(x) + log(x-3) = 2·log(2)

Use this rule of logs 

log(A) + log(B) = log(AB)

to rewrite the left side,

and the rule 

N·log(A) = log(AN) to rewrite
the right side:

   log[x(x-3)] = log(22)

   log[x(x-3)] = log(4)

Take "anti-logs" of both sides

        x(x-3) = 4 

       x² - 3x = 4

Get 0 on the right:

   x² - 3x - 4 = 0

Factor the left side:

(x - 4)(x + 1) = 0  

Set each factor on the left = 0

x - 4 = 0 gives x = 4

X + 1 = 0 gives x = -1

We discard the negative answer because
the original equation contains log(x)
and logs may only be taken of positive
numbers.

Edwin
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