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A value of $x$ that satisfies the equation $\log x + \log (x – 7) = \log (x + 11) + \log 2$ is

(A) 1 (B) 2 (C) 7 (D) 11

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$\log m + \log n = \log mn$

So, $\log x + \log (x-7) = \log (x+11) + \log 2$

$\Rightarrow \log x(x-7) = \log 2 (x+11)$

$\Rightarrow x(x-7) = 2 (x+11)$

$\Rightarrow x^2-9x-22=0$

$\Rightarrow (x-11)(x+2)=0$

$\therefore x=11$

$\because x \neq -2$ , log is undefined for negative number.

answered by Veteran (53.6k points)
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