Solve :
$2 {log}_{10} (2 x) = {log}_{10} (7 x - 2 - 2 x^{2})$

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Solution

according to question,

$\Rightarrow$ $2 l o g_{10} (2 x) = l o g_{10} (7 x - 2 - 2 x^{2})$

$\Rightarrow$ $l o g_{10} (2 x)^{2} = l o g_{10} (7 x - 2 - 2 x^{2})$

$\Rightarrow$ $(2 x)^{2} = 7 x - 2 - 2 x^{2}$

$\Rightarrow$ $4 x^{2} = 7 x - 2 - 2 x^{2}$

$\Rightarrow$ $6 x^{2} - 7 x + 2 = 0$

$\Rightarrow$ $x = \frac{1}{2}, \frac{2}{3}$

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