solve-3-x-3-72x-39-9-3-log-7-x-0-

Question Number 172085 by Mikenice last updated on 23/Jun/22

s o l v e

(3^{x^{3} - 72 x + 39} - 9 \sqrt{3}) \times l o g (7 - x) = 0

Answered by mr W last updated on 23/Jun/22

\log (7 - x) = 0 \Rightarrow 7 - x = 1 \Rightarrow x = 6

o r

3^{x^{3} - 72 x + 39} - 9 \sqrt{3} = 0

3^{x^{3} - 72 x + 39} = 9 \sqrt{3} = 3^{2 + \frac{1}{2}}

x^{3} - 72 x + 39 = 2 + \frac{1}{2}

x^{3} - 72 x + \frac{73}{2} = 0

\Rightarrow x = 4 \sqrt{6} \sin (\frac{1}{3} \sin^{- 1} \frac{73 \sqrt{6}}{1152} + \frac{2 k π}{3}) (k = 0, 1, 2)

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