Question

as quick as possible

Answer 1

Answer:

option: (c) 2

Explanation:

( \frac{ ln(e {x}^{2} ) }{ ln( \frac{e}{ {x}^{2} } ) } )^{2} = \frac{1 + \sin \frac{2\pi}{7} }{( \sin \frac{\pi}{7} \cos \frac{\pi}{7} )^{2} } \\( \frac{ ln(e {x}^{2} ) }{ ln( \frac{e}{ {x}^{2} } ) } )^{2} = \frac{1 + \sin \frac{2\pi}{7} }{sin^{2} \frac{\pi}{7} + cos^{2} \frac{\pi}{7} +2.sin \frac{\pi}{7} .cos \frac{\pi}{7} } \\ ( \frac{ ln(e {x}^{2} ) }{ ln( \frac{e}{ {x}^{2} } ) } )^{2} = \frac{1 + sin \frac{2\pi}{7} }{1 + sin \frac{2\pi}{7} } = 1 \\ \frac{ ln(e {x}^{2} ) }{ ln( \frac{e}{ {x}^{2} } ) } = 1 \\ ln(e {x}^{2} ) = ln( \frac{e}{ {x}^{2} } ) \\ e {x}^{2} = \frac{e}{ {x}^{2} } \\ {x}^{4} = 1

So this equation has two real solutions.