Find-2-log-5-sin-pi-7-log-sin-7-5-

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

Find : 2 \log_{\sqrt{5}} \sin \frac{π}{7} \cdot \log_{\sqrt{\sin \frac{π}{7}}} 5 = ?

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

= 2 \times \frac{\log (\sin \frac{π}{7})}{\frac{\log 5}{2}} \times \frac{\log 5}{\frac{\log (\sin \frac{π}{7})}{2}}

= 8 \times \frac{\log (\sin \frac{π}{7})}{\log 5} \times \frac{\log 5}{\log (\sin \frac{π}{2})}

= 8

Commented by hardmath last updated on 02/Jun/24

thank you dear professor