Question

Solve for x:
$2\log_{10} x = 1+\log_{10} (x+\frac{11}{10})$

Answer 1

$2 log(x) = 1 + log(x + \frac{11}{10} ) \\ log( {x}^{2} ) = log(10) + log(x + \frac{11}{10} ) \\ log( {x}^{2} ) = log(10(x + \frac{11}{10} )) \\ {x}^{2} = 10x + 11 \\ {x}^{2} - 10x - 11 = 0 \\ (x - 11)(x + 1) = 0 \\ x = 11$
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