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If $\log_{10} (x - 9) + \log_{10} x = 1,$ then $x =$

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$- 1$

$10 o r - 1$

answer is C.

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Detailed Solution

$\log_{10} x (x - 9) = 1,$

$x (x - 9) = 10$

$x^{2} - 9 x - 10 = 0$

$x^{2} - 10 x + x - 10 = 0$

$x (x - 10) + 1 (x - 10) = 0$

$(x - 10) (x + 1) = 0$

$x = 10 or x = - 1$

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