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Question Number 208037 by hardmath last updated on 02/Jun/24

$$\mathrm{Find}:2{\log }_{\sqrt{5}}\sin \frac{\pi }{7}\cdot {\log }_{\sqrt{\mathbf{sin}\frac{\mathit{\pi }}{7}}}5=?$$

Answered by mr W last updated on 02/Jun/24

$$=2\times \frac{\log \left(\sin \frac{\pi }{7}\right)}{\frac{\log 5}{2}}\times \frac{\log 5}{\frac{\log \left(\sin \frac{\pi }{7}\right)}{2}}$$$$=8\times \frac{\cancel{\log \left(\sin \frac{\pi }{7}\right)}}{\cancel{\log 5}}\times \frac{\cancel{\log 5}}{\cancel{\log \left(\sin \frac{\pi }{2}\right)}}$$$$=8$$

Commented by hardmath last updated on 02/Jun/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

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