Question

помогите с подробным решением

Answer 1

$1); ; left { {{log_3x+log_3y=log_34+2} atop {2^{log_2(x+y)}=5log_216}} right. ; ,quad ODZ:; ; x>0; ,; y>0$

$left { {{log_3(xy)=log_34+log_33^2} atop {x+y=log_2(2^4)^5}} right. ; left { {{log_3(xy)=log_3(4cdot 9)} atop {x+y=log_22^{20}}} right. \\ left { {{xy=36} atop {x+y=20}} right. ; left { {{x(20-x)=36} atop {y=20-x}} right. ; left { {{x^2-20x+36=0} atop {y=20-x}} right. ; left { {{x_1=2; ,; x_2=18} atop {y_1=18; ,; y_2=2}} right. \\Otvet:; ; (2,18); ,; ; (18,2)$

$2); ; 4^{frac{1}{2}log_23+3log_85}=(2^2)^{frac{1}{2}log_23+3log_{2^3}5}=2^{log_23+2log_25}=\\=2^{log_23+log_25^2}=2^{log_2(3cdot 25)}=3cdot 25=75$