Question

Помогите решить!!
1)-12cos36/sin^2 18-cos^2 18
2)38cos153/cos27
3)log_4(3x+7)=2log_4 3

Answer 1

$frac{12cos 36^{0} }{ sin^{2}18 ^{0} - cos^{2} 18^{0} }= frac{12cos 36^{0} }{-( cos^{2} 18^{0}- sin^{2} 18 ^{0} )} = frac{-12cos 36^{0} }{-cos(2* 18^{0} )} = frac{-12cos 36^{0} }{-cos 36^{0} }=12$
$frac{38cos 153^{0} }{cos 27^{0} }= frac{38cos (180^{0}- 27^{0}) }{cos27 ^{0}} = frac{38*(-cos 27^{0} )}{cos 27^{0} } =-38$
log₄(3x+7)=2*log₄3,  log₄(3x+7)=log₄3²
log₄(3x+4)=log₄9
$left { {3x+7 textgreater 0}} atop {3x+7=9}} right., left { {{3x textgreater -7} atop {3x=2}} right. , left { {{x textgreater - frac{7}{3} } atop {x= frac{2}{3} }} right.$
ответ: x=2/3