log-x-3-3x-54-log-3-x-18-3log-x-3-x-2-x-

Question Number 161362 by cortano last updated on 17/Dec/21

\log_{\sqrt{\frac{x}{3}}} {(3 x - 54)}^{\log_{3} (x)} = 18 - 3 \log_{\frac{x}{3}} (x^{2})

x = ?

Commented by bobhans last updated on 17/Dec/21

\frac{\log_{3} (x) [1 + \log_{3} (x - 18)]}{\frac{1}{2} [\log_{3} (x) - 1]} = 18 - \frac{6 \log_{3} (x)}{\log_{3} (x) - 1}

\frac{2 \log_{3} (x) [1 + \log_{3} (x - 18)]}{\log_{3} (x) - 1} = \frac{12 \log_{3} (x) - 18}{\log_{3} (x) - 1}

2 \log_{3} (x) + 2 \log_{3} (x) \log_{3} (x - 18) = 12 \log_{3} (x) - 18

\log_{3} (x) \log_{3} (x - 18) - 5 \log_{3} (x) + 9 = 0

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