Question

find value of x
$log_{3 }(x) + 2 \times log_{x}(3) = 3$
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Answer 1

Step-by-step explanation:

$\frac{1}{ log_{x}(3) } + 2 \times log_{x}(3) = 3 \\ lets \: log_{x}(3) = t \\ \frac{1}{t} + 2t = 3 \\ 2 {t}^{2} - 3t + 1 = 0 \\ 2 {t}^{2} - 2t - t + 1 = 0 \\ 2t(t - 1) - 1(t - 1) = 0 \\ t = \frac{1}{2} \: \: \: and \: \: \: t = 1 \\ log_{x}(3) = \frac{1}{2} \: \: \: and \: \: log_{x}(3) = 1 \\ x = 9 \: \: \: and \: \: \: x = 3$

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