Question

Решить систему: log_y(x)-log_2(y^2)=1, log_4(x)-log_4(y)=1.

Answer 1

log(4)x-log(4)y=1⇒log(4)x/y=1⇒x/y=4⇒x=4y
log(y)4y-log(2)y²=1
1+2log(y)2 -2/log(y)2=1
log(y)2+2log²(y)2-log(y)2-2=0    log(y)2≠0
2log²(y)2=2
log²(y)2=1
log(y)2=-1 U log(y)2=1
y1=1/2 U y2=2
x1=2 U x2=8
(2;1/2) U (8;2)