The bigger value of $x$ that satisfies the equation ${log}_{2} (3 x - 1) - 2 {log}_{2} x = 1$ is

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Solution

${log}_{2} (3 x - 1) - {log}_{2} (x^{2}) = 1$
Or
${log}_{2} (\frac{3 x - 1}{x^{2}}) = 1$
Or
$(\frac{3 x - 1}{x^{2}}) = 2$
Or
$2 x^{2} - 3 x + 1 = 0$
Or
$2 x^{2} - 2 x - x + 1 = 0$
Or
$2 x (x - 1) - (x - 1) = 0$
Or
$(2 x - 1) (x - 1) = 0$
Or
$x = 0.5, 1$
Hence the answer is $x = 1$

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