Solution 3.4:3c
From Förberedande kurs i matematik 1
With the log laws, we can write the left-hand side as one logarithmic expression,
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but this rewriting presupposes that the expressions 0
0
we must remember to permit only solutions that satisfy 0
0
The equation rewritten in this way is, in turn, only satisfied if the arguments
We rewrite this equation as
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which means that 2
Because \displaystyle x=-3 is negative, we neglect it, whilst for \displaystyle x=1 we have both that \displaystyle x > 0 and \displaystyle x(x+4) = 2x+3 > 0\,. Therefore, the answer is \displaystyle x=1\,.