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Question Number 154748 by imjagoll last updated on 21/Sep/21

Answered by ARUNG_Brandon_MBU last updated on 21/Sep/21

$$\sin \left({3\log }_{\left(2\sin x\right)}\sqrt[3]{\pi }\right)=\frac{1}{2}\Rightarrow {\log }_{\left(2\sin x\right)}\pi =\frac{\pi }{6}$$$$\Rightarrow {\log }_{\pi }\left(2\sin x\right)=\frac{6}{\pi }\Rightarrow \sin x=\frac{1}{2}{\pi }^{\frac{6}{\pi }}$$$$\Rightarrow x=\arcsin \left(\frac{1}{2}{\pi }^{\frac{6}{\pi }}\right)$$

Commented by mathdanisur last updated on 21/Sep/21

$$\mathrm{and}\mathrm{x}=\pi -\arcsin \left(\frac{1}{2}{\pi }^{\frac{6}{\mathit{\pi }}}\right)+2\pi n$$

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