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Log x + log(x+3) = 1

User Neverlord
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1 Answer

4 votes

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Answer:

x = 2

Explanation:

Taking antilogs, the equation becomes ...

x(x +3) = 10

x^2 +3x +2.25 = 12.25 . . . . add (3/2)² to complete the square

(x +1.5)² = 3.5² . . . . write as squares

x = -1.5 +3.5 . . . . . . take the positive square root*

x = 2

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* The negative square root gives an extraneous solution (x=-5).

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I find that using a graphing calculator with the original equation avoids extraneous solutions. Here we transform the equation to the form f(x) = 0, so the x-intercept is the value of x we seek.

Log x + log(x+3) = 1-example-1
User Lucas Bernalte
by
4.3k points