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

  1. $1$ 
  2. $2$ 
  3. $7$ 
  4. $11$
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2 Answers

Best answer
12 votes
12 votes
$\log m + \log n = \log mn$

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.

Correct Answer: $D$
edited by
1 votes
1 votes
Another approach try substitution of all the answers 1,2,7 doesn't satisfy the equation as value of log is never negative and zero.

So answer is 11 so lets substitute 11 and verify.

log 11+log 4=log(22)+log 2

log(22)=log(11*2)=log(11)+log(2)

log 11+ log 4=log 11+ log 2+ log 2

log 11+ log 4= log 11 + 2 log 2

log 11 + 2 log 2= log 11 + 2 log 2

LHS = RHS
Answer:

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