MathDB
1968 AMC 12 #23 - Logarithmic Equation

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January 1, 2012
logarithmsAMC

Problem Statement

If all the logarithms are real numbers, the equality log⁡(x+3)+log⁡(x−1)=log⁡(x2−2x−3) \log(x+3)+\log (x-1) = \log (x^2-2x-3) is satisfied for:
<spanclass=′latex−bold′>(A)</span> all real values of x<spanclass=′latex−bold′>(B)</span> no real values of x<spanclass=′latex−bold′>(C)</span> all real values of x except x=0<spanclass=′latex−bold′>(D)</span> no real values of x except x=0<spanclass=′latex−bold′>(E)</span> all real values of x except x=1<span class='latex-bold'>(A)</span>\ \text{all real values of}\ x \\ \qquad<span class='latex-bold'>(B)</span>\ \text{no real values of}\ x \\ \qquad<span class='latex-bold'>(C)</span>\ \text{all real values of}\ x\ \text{except}\ x=0 \\ \qquad<span class='latex-bold'>(D)</span>\ \text{no real values of}\ x\ \text{except}\ x=0 \\ \qquad<span class='latex-bold'>(E)</span>\ \text{all real values of}\ x\ \text{except}\ x=1
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